Answer:
Yes, the objective is met by the woman with the bank plan.
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 × [tex](1+\frac{r}{n} )^{n*t}[/tex]
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 × [tex](1+\frac{0.12}{1})^{15}[/tex]
FV = 100,000 × [tex](1.12)^{15}[/tex] = $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.
