A small business owner contributes $4,000 at the end of each quarter to a retirement account that earns 10% compounded quarterly.

Question

(a) How long will it be until the account is worth at least $150,000? (Round your answer UP to the nearest quarter.)

(b) Suppose when the account reaches $150,000, the business owner increases the contributions to $8,000 at the end of each quarter. What will the total value of the account be after 15 more years? (Round your answer to the nearest dollar.)

Answer 1

·(a) 150000 = 4000[(1 + 0,025)^4t - 1]/0.025; 0.9375 + 1 = 1.025^4t, t = ln1.9375/(4ln1.025) = 6.75 years = 27 quarters

(b) A = 150000·1.025⁶⁰ + 8000(1.025⁶⁰ - 1)/0.025 = $1,747,901