Question

If Derek plans to deposit $10,746.00 into his retirement account on each birthday beginning with his 26th and the account earns 11.00%, how long will it take him to accumulate $2,906,805.00?

Answer format: Number: Round to: 2 decimal places

Answer 1

Future value of annuity = P * [(1+R)^N-1]/R

Where, P = Payment

R = Rate of interest

N = Number of periods

2906805 = 10746 * [(1+11%)^N-1]/11%

2906805 /10746 = [(1.11)^N-1]/0.11

270.501116695 * 0.11 = (1.11)^N-1

29.7551228365 + 1 = (1.11)^N

30.7551228365 = (1.11)^N

Now, We will use hit and trial method to arrive at approximate value of N

30.7551228365 = (1.11)^32.83

Therefore, Value of N = 32.83 years