Question

A woman can invest $100 000 for 15 years in a bank and expect to receive a yearly return of $10 000. The woman's objective is to earn 12% per year, compounded annually, on her investments. Is this objective met by the bank plan?

Answer 1

Yes, the objective is met by the woman with the bank plan.

Step-by-step explanation:

To determine is the woman meets her objective, we will calculate the future value on the amount invested after 15 years with an annual compound interest, as shown:

FV = PV ×
`(1+(r)/(n) )^(n*t)`

where:

FV = future value = ???

PV = present value = $100,000

r = interest rate in decimal = 12% = 0.12

n - number of compounding period per year = annual = 1

t = compounding period in years = 15

Therefore:

FV = 100,000 ×
`(1+(0.12)/(1))^(15)`

FV = 100,000 ×
`(1.12)^(15)` = $547,356.58

Next from the future value, we can calculate the interest, by subtracting the present value from the future value as follows:

Interest = future value - present value = 547,356.58 - 100,000

= $447,356.58

To calculate the interest earned per year for 15, years, we will divide the total interest by 15 :

interest earned per year = 447,356.58 ÷ 15 = $29,823.77

Hence, since th woman set out to earn $10,000 per year, but she ended up earning $29,823.77 per year, her objective was met and even more.