Question

What initial investment must be made to accumulate $60000 in 17 years if the money is invested in a mutual fund that pays 12% annual interest, compounded monthly?

Answer 1

$7881.18

Step-by-step explanation:

   Let the initial Investment be $P_{0}$. The Interest is compounded on a monthly basis at 12% annual interest rate. After 17 years, the Investment amounts to $60,000.

   As the annual interest rate is 12%, the monthly interest rate is 1%.

Since this is a compound interest problem, the total amount can be modeled as follows: $P(t)=P_{0}(1+\frac{i}{100})^{t}$

Here $i$ is the interest rate, i.e $1$, and t is the number of time periods, i.e $17\textrm{ years x }12\frac{\textrm{months}}{\textrm{year}}$= $204\textrm{ months}$

$60,000=P_{0}\textrm{ x }(\frac{101}{100})^{204}$

$P_{0}=7881.18$

∴ Initial Investment = $7881.18