Question

Determine how much money would be in a savings account that started with a deposit of $2000 in year 1 and each succeeding amount increasing by 10% per year, use an interest rate of 8% per year and a 20 year period 4. An investment of $6000 increased to $10,000 over a 5-year period. What was the annual rate of return on the investment? 5.

Answer 1

4. Present value of geometric series = C*[(1+g)^n / (1+i)^n - 1] / (g-i)

Here C = 2000

g = 0.1

i = 0.08

n = 20

P = 2000*[(1+0.1)^20 / (1+0.08)^20 - 1] / (0.10-0.08)

P = 2000*[(1.1)^20 / (1.08)^20 - 1] / (0.02)

P = 2000 * 22.168652

P = 44337.31

F = 44337.31 * (1+0.08)^20 = 44337.31 * 4.660957 = 206654.30

5.

F = 10000, P = 6000, t = 5 yrs

using formula F = P*(1+i)^t

10000 = 6000*(1+i)^5

(1+i)^5 = 10000 / 6000 = 1.6667

1+i = 1.6667 ^(1/5) = 1.107566

i = 0.107566

i = 10.76%