Interest Question

Question

If somebody owes \$55k and pays it back in four years with 6.4% interest p.a, how much would it be if its compounded quarterly?

So I used $$A=P(1+i/4)^{4(4)}$$ and plugged it in as $$A=55000(1+.064/4)^{16}$$ but my answer was \$591,000? And I'm sure it's wrong so can someone please help explain what I did wrong?

Answer 1

Hint: You have to calculate

$C_4=C_0\cdot \left(1+\frac{i}{m} \right)^{m\cdot n}= \$55,000\cdot \left(1+\frac{0.064}{4} \right)^{4\cdot 4}=\$70,902.58$

$\frac{0.064}{4}$ is the the quarterly interest rate. And n the amount of years. And m is the frequency of compounding (per year).

Remark: As Padding Ghost commented, you have inserted 0.64 instead of 0.064.

Answer 2

As there is only 1 problem with your work, this answer will be short. It seems you have mistakenly typed in $.64$ instead of $.064$. This agrees with you're original value. That is, $55000(1+.64/4)^{16} \approx 591,000$. The correct value is obtained when you hit the right buttons and do the calculation $55000(1+.064/4)^{16} \approx 70900$.

Edit: In the case that this is actually meant to be a loan repayment/annuity problem. My answer will not give you the correct answer. Please see the answer that paw88789 gives.

Answer 3

Assuming that you are making quarterly payments, rather than a single payment at the end, you would use the present value of an annuity formula:

$ \$55000 = R\cdot\frac{1-1.016^{-16}}{.016}$

To find the quarterly payment size, $R$.