Question

Ansh plans to save for her retirement savings at the end of each quarter for 11 years. The first investment is $2500 and she plans to increase the investment amount by 0.5% per quarter thereafter. Assume her investments can earn 9% compounded quarterly. Round final answers to the nearest cent. a) How much money will Ansh have at the end of 11years? b) What will be the investment amount of her last savings contribution?

Answer 1

Question a:

P = First payment = $2,500

n = 11*4 = 44 Quarters

g = growth rate = 0.5%

r = interest rate = 9%/4 = 2.25%

Amount at the end of 11 years = [P / (r-g)] * [(1+r)^n - (1+r)^n]

= [$2,500 / (2.25%-0.5%)] * [(1+2.25%)^44 - (1+0.5%)^44]

= [$2,500 / 0.0175] * [2.66186444 - 1.24539385]

= [$2,500 * 1.41647059 / 0.0175]

= $202,352.942

Therefore, amount at the end of 11 years is $202,352.94

Question b:

Last savings constribution = P * (1+r)^n

= $2,500 * (1+0.5%)^44

= $2,500 * 1.24539385

= $3,113.48462

Therefore, last savings contribution to the retirement plan is $3,113.48