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?

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