## Calculating the Growth Rate of an Investment 141-30.a

This video is provided as supplementary
material for courses taught at Howard Community
College and in this video I’m going to show how to calculate the
growth rate of an investment. The problem says An investment \$4000
grows to \$6800 in 10 years. What annual nominal rate would produce the same growth if the
interest was compound annually, or compounded monthly or compounded continuously. Let’s
start with the compounded annually problem. We want to find out what interest rate we would have to get if
we invested \$4000 compounded annually for 10 years and wanted it to grow to \$6800. So the formula we have for compound interest is A equals P times 1 plus r/n raised to the nt power. Now A is the amount of
money that we’re getting back. We want to get back 6800. So we’ll replace A with 6800. And P is the principal, which is the \$4000 we
would invest initially. we’ve got 1 plus r/n. r is the interest rate. We don’t know that
so we’ll just write r, and n is the number of compounding
periods per year. Well, if its compounded annually there’s only one compounding period each year. So n would be 1. So this is just (1 + r),
and then we’re raising that to the nt power, where t is time and we want this to happen over a 10-year period. Once again n equals 1. So this is raised to the 10th
power. Now what we have to do is solve for r.
The first thing is to divide both sides of the equation by 4000. So I’ve got 6800 divided by 4000, and that equals 1.7. Now I have 1.7 equals (1 + r) raised to the 10th power. I’d like to get rid
of this exponent. I’ll raise the entire right side of the equation to another power, 1/10, and then the 10 and the
1/10 will cancel each other out. I have to do the same thing to the left
side of the equation. So the left side become 1.7 raised to the 1/10. This means I’ll have 1.7 raised to the one-tenth power and that will equal 1 + r. Let’s finish getting the r all by itself. I’ll just subtract 1 from both
sides of the equation. So it’s 1.7 raised to the 1/10 – 1. I’ll use a calculator. I want 1.7 raised to the 1/10. When I get an answer I subtract 1 from
that, and what I end up with is .05449, and that it equals r. So we’ve got to round this and turn it into a percent. I’ll multiply
by 100. that will give me 5.45%. So the answer to the first part of the
problem is we have to invest this money at 5.45%. Now let’s go on to the next part. This is
where the money is invested and compounded monthly. So we’ll have that same
formula again, A equals P times 1 plus r/n raised to the nt power. A, once again, is 6800, and P is 4000. We multiply that times 1 plus r/n — we don’t know what r is, but n, the number of compounding periods a year, would be 12, because we’re compounding monthly. That’s raised at to the nt power. n is 12, and t is the number of years,
that’s 10. And now we want to solve for r. I’ll divide both sides by 4000.
When I did that last time I got 1.7. So 1.7 equals 1 plus r/12 raised to the 12 times
10, which is 120. I want to get rid of the exponent. So I’ll raise both sides of the equation to the 1/120 power. I have 1.7 raised to the 1/120 equals 1 + r/12. I’ll subtract 1 from both
sides of the equation. I have 1.7 to the 1/120 minus 1 equals r over 12. To get r, we’ll just multiply both
sides the equation by 12. So I have 12 times 1.7 raised to the 1/120 -1 equals r. I’ll use the calculator. First I’ll do 1.7 raised to the 1 divided by 120. I’ll subtract 1 from the answer. And now I want to take that, that’s
everything here in parentheses, and multiply it by 12. and I end up with .05318… I’ll turn this into a percent and round it. So it’s going to be 5.32%. This is a little bit lower than what we
got the last time. That was 5.45%, which makes sense because we’re compounding more frequently. And the last one is what happens when we compound
continuously. We have a different formula for that. The formula of compounding continuously
is A equals P times e raised to the rt. So, A once again is 6800. P is 4000, and I’ve got that raised to the rt. I don’t know what r is, but I know t is
10. So that’s the r times 10, or 10r power. I want to solve for r, so I’ll take the
natural log of both sides of this equation……. Oh, I’m sorry, first I should divide both sides by 4000. That’s the samething I’ve done twice already. I get 1.7 equals e to the 10r. Now we’ll take the natural logs. So I
have ln, the natural log, of 1.7 equals the natural log of e raised to the 10r. I can take this exponent, 10r, and using exponent rule for logarithms, make that into a coefficient. So I have the natural log of 1.7 equals 10r times in the natural log of e. But the natural log of e is just 1. So I’ll cross that out. I have the natural log of 1.7 equals 10r. I’ll divide both sides by 10 and I get the rate is the natural log
of 1.7 divided by 10. Let’s use a calculator to find that
natural log of 1.7. And I want to divide that by 10. and I get .05306… for the rate. We’ll round this and turn it
into a percent. It’s going to be 5.31%, a little bit lower than the
previous rate because it’s compounded continuously.
okay And that’s it. Take care. I’ll see you next
time.

## Business Cycles Explained: Austrian Theory

The Austrian theory postulates that entrepreneurs
are tricked or fooled by government-engineered increases in the money supply. Here’s a
simple example of how the scenario runs: The central bank inflates the supply of money.
The real interest rate falls because there are more funds to be lent out. As the real
interest falls, entrepreneurs borrow more. They undertake longer and more ambitious projects,
and eventually, according to the Austrian theory, those longer and more ambitious projects
cannot be sustained, they turn a loss rather than a profit, and eventually the boom becomes
a bust. [The Housing Bubble] To consider a specific example, it’s been
argued by many Austrians that the housing bubble was in fact an illustration of Austrian
business cycle theory. In the years 2001 to 2004, the Fed really was somewhat loose with
credit, nominal interest rates were quite low, there was a housing bubble. People borrowed
a lot more money; they borrowed more than they should have. People thought the good
conditions, the low interest rates on mortgages, the easy availability of credit, and the rising
home prices would continue forever. That wasn’t the case. Eventually the bubble burst, these
trends were reversed, and we had a lot of long-term construction projects and housing
and mortgage decisions that turned out in retrospect to have been big mistakes. [Austrian Remedies] Austrians propose some different remedies
for stopping the problem in the first place. To stop the problem in the first place, Austrians
have argued we should either have a gold standard or tighter money or some kind of monetary
rule. The belief is it would then be harder to fool entrepreneurs because, in terms of
monetary conditions, it is believed they would be more stable or at least entrepreneurs would
know what to expect. [Explaining the Great Recession] Austrians and Keynesians give very different
readings of the 1920s and the subsequent Great Depression. According to a lot of Keynesians
and also monetarists, there’s some critical negative period between 1929 and 1932, and
a much stronger economy. The Austrian view is different. According to the Austrians there
was a lot of loose money and monetary expansion in the 1920s. Entrepreneurs took on projects
which were too ambitious, and once those longer-term projects are in place, Austrians often believe
there’s not any way you can back out of the jam you’re in, that a lot of those investments
will turn bad. Now on this question I’m not actually so much of an Austrian when it
comes to the Great Depression, but that’s one way of thinking about the difference between
the two points of view. Austrians locate the problem more in a kind of original sin of
inflation, which once it has been committed is very hard to get out of. Monetarists and Keynesians tend to think that
if you can boost aggregate demand or maintain aggregate demand at the proverbial last minute
that you’ll actually succeed in making the cycle a much less severe one. [Strengths and Weaknesses] Strengths and weaknesses of the Austrian theory:
What are they? I think one strength is that we do see a lot of credit bubbles in history,
and on average those credit bubbles are associated with periods of loose monetary policy. The
Austrian theory picks up some important part of this story. There is too much credit put
on the market, entrepreneurs are fooled, and this is one factor that contributes to making
for a recession or depression. But the Austrian theory also has some weaknesses. One is that
for a theory which stresses the virtues of the market, it assumes that entrepreneurs
are tricked rather easily. So say there’s some inflation or an increase in credit. An
entrepreneur doesn’t have to be genius to say, “Hey wait a minute, there’s been
some inflation. I saw this on Fox News; I read about it in the Wall Street Journal.
Maybe I shouldn’t overexpand my business. There’s some inflation. Maybe now is time
to just be a little more cautious.” It’s also the case that looking back in history,
a lot of business cycles are caused by monetary contractions and not by the previous expansion.
So there’s an awful lot of cases where the Austrian theory wouldn’t even potentially
apply.

## NEWS: Alliance banks on SMEs as loans slow

long growth target for the new financial year is a 7% overall obviously the focus will be primarily on SME and consumer in an SME we will aim to get closer to 10% growth in terms of the long growth we had targeted you're right we had targeted 10% for FY 19 and we ended up at 6% the reason for the difference primarily was because in our commercial in corporate book the the longer man was substantially lower due to due to the effect of the slowdown especially of key large projects while at the same time actually we exceeded our goals in in SME for FY 2010 you to see headwinds although we do see that the momentum for SME stays very strong in terms of the overall outlook we note that the economy is a little bit more challenged right now and we see a little bit of headwinds we think we're going to continue to be able to grow the business and to serve our consumer and SMEs especially better we have a lot of developments in the pipeline to do that