Question

For twenty-eight years beginning on their 25th birthday an individual deposits $100 each month into an account which pays 4.6% interest compounded continuously. How much will be in the account on their 62nd birthday?

Answer 1

Monthly Deposits = P = $100

Number of deposits made = n = 28*12 = 336

Interest rate = r = 4.6%/12

FV = Pe^(n-1)r +....+ Pe^2r + Pe^1r + P = P (e^rt - 1)/(e^r - 1) = 100*(e^{(336*0.046/12)} - 1)/(e^(0.046/12) - 1) = $68360.85

Hence, amount in account at 62nd birthday = $68,360.85