Q:

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?

Accepted Solution

A:
$7881.18Step-by-step explanation:    Let the initial Investment be [tex]P_{0}[/tex]. 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: [tex]P(t)=P_{0}(1+\frac{i}{100})^{t}[/tex]Here [tex]i[/tex] is the interest rate, i.e [tex]1[/tex], and t is the number of time periods, i.e [tex]17\textrm{ years x }12\frac{\textrm{months}}{\textrm{year}}[/tex]= [tex]204\textrm{ months}[/tex][tex]60,000=P_{0}\textrm{ x }(\frac{101}{100})^{204}[/tex][tex]P_{0}=7881.18[/tex]∴ Initial Investment = $7881.18