Question

if derek plans to deposit $12,761 into his retirement account on each birtbday behinning with his 26th and the account earns 12% ,how long will it take him to accumulate $2,383,552?

Answer 1

- Periodic annual deposit into retirement account = $12,761

Accumulated value of account = $2383,552

Calculating the no of years it will take to accumulate the account:-

Where, C= Periodic Deposits = $12,761

r = Periodic Interest rate = 12%

n= no of periods

Future Value = $2383,552

20.01258298 = (1.12)^n

Taking Log on both sides,

Log(20.01258298) = n*Log(1.12)

1.301303146 = n*0.049218023

n = 26.44

If you need any clarification, you can ask in comments.     

If you like my answer, then please up-vote as it will be motivating