Question

David inherited an annuity worth $4,169.87 from his uncle. The annuity will pay him five equal payments of $1,100 at the end of each year. The annuity fund is offering a return of _______.

David's friend, Sagar, wants to go to business school. While his father will share some of the expenses, Sagar still needs to put in the rest on his own. But Sagar has no money saved for it yet. According to his calculations, it will cost him $55,142 to complete the business program, including tuition, cost of living, and other expenses. He has decided to deposit $5,000 at the end of every year in a mutual fund, from which he expects to earn a fixed 9% rate of return It will take approximately _____ years for Sagar to save enough money to go to business school.

Answer 1

a). To find the rate of return, we need to put the following values in the financial calculator:

N = 5; PV = 4169.87; PMT = -1100; FV = 0;

Press CPT, then I/Y, which gives us 10

So, Rate of Return = 10%

b). FV of Annuity = Annual Deposit * [{(1 + r)ⁿ - 1} / r]

$55,142 = $5,000 * [{(1 + 0.09)ⁿ - 1} / 0.09]

$55,142 / $5,000 = [{(1.09)ⁿ - 1} / 0.09]

11.0284 * 0.09 = (1.09)ⁿ - 1

0.992556 + 1 = (1.09)ⁿ

log(1.992556) = n[log(1.09)]

0.6894 = n[0.0862]

n = 0.6894 / 0.0862 = 8

So, It will approximately 8 years