0
$\begingroup$

So I have this maths question which I am struggling to solve as it seems to be a backwards compound interest or possibly an annuity question. I was wondering whether anyone might be able to provide a hint as to how I can do this question as from what I can tell you have to calculate the total amount of money you would have used at the end of 18 years after investing the money yet taking out payments every time. I am just unsure how to go about doing this and any help would be greatly appreciated.

You invest your superannuation of $100 000 into a bank account in which you get 3% p.a. for 18 years. You decide that you want to get monthly payments of this money over the 18 years. How will you have received by the end of 18 years?

$\endgroup$
1
  • $\begingroup$ is the per-annum APY or APR ? $\endgroup$ – user451844 Sep 5 '17 at 21:22
1
$\begingroup$

Let be $S_0=100,000$ your initial amount of money, $i^{(12)}=3\%$ the interest rate convertible monthly, $n=18$ the number of years and $m=12n $ the number of months. Let be $P$ the monthly withdrawal.

The monthly interest rate is $$i=\frac {i^{(12)}}{12}$$

Without withdrawals the final sum after $m $ months will be $$ S_m=S_0 (1+i)^m $$ The monthly withdrawals of $P $ is equivalent to an annuity that will produce a future value of $$ W_m=P\, s_{\overline{m}|i}=P\,\frac{(1+i)^m-1}{i} $$ and then the future value of $S_0$ with monthly withdrawals $P $ will be $$ S=S_m-W_m=S_0 (1+i)^m-P\,\frac{(1+i)^m-1}{i} $$ You might also think in terms of present value and obtain $$ S=\left( S_0-P\, a_{\overline{m}|i}\right)\times (1+i)^m $$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.