Video Transcript
An investment account offers an
annual rate of interest of five percent, compounded monthly. Amera invests 6000 dollars in
this account. How much will she have in the
account after seven years? Compare this to the amount she
would have if the interest were only compounded once a year.
Okay, so let’s pick out the
important information. The annual interest rate is
five percent. And its compounded monthly, so
that means that 𝑛 is 12. We’re gonna have 12 bits of
compounding going on per year. She’s investing 6000 dollars in
the account. And she’s gonna have it for
seven years. Well, the formula for the final
value is 𝑣 is equal to 𝑝 times one plus 𝑟 over 100 all over 𝑛 all to the
power of 𝑦 times 𝑛.
So, let’s think about this. 𝑛 was equal to 12, there was-
it was compounded monthly. So, that’s 12 times a year. 𝑟 is five; the rate of
interest is five percent per year. 𝑦 equals seven because we’re
talking about seven years. And the principal, the initial,
amount invested was 6000 dollars.
Well, replacing all those
letters in the formula with the numbers that we’ve just put there, we’ve got 𝑣,
the final value, is equal to 6000 times one plus five over 100 all divided by 12
all to the power of seven times 12. So, popping all that into the
calculator and then rounding our answer to two decimal places because we’re
talking about money, that gives us 8508 dollars and 22 cents. So, with monthly compounding,
we will end up with 8505 dollars and 22 cents in the account. Now, we’ve got to compare that
with annual compounding.
So, the formula for annual
compounding, we still got our initial principal sum of 6000 dollars. And the multiplier one plus
five over 100 is 1.05, so we’re adding five percent every year. And we’re just doing that at
the end of the year. And we’re doing that seven
times here, so the power there is seven. If we put that into our
calculator, we only get 8442 dollars and 60 cents, rounding to two decimal
places.
So, comparing this amount to
the amount that she’d have got for the interest being compounded only once a
year, she’s got 65 dollars and 62 cents more than if the interest were only
compounded once a year. So, that’s the difference
between those two amounts. So, it’s worth pointing out
then, that looking at how often these things are compounded can make quite a big
difference to the amount of money that you get back on your savings. So, it’s definitely worth
checking out.
