Question

Suppose you start saving for retirement by depositing $4,000 EVERY YEAR into your retirement account. If your annual return is 8%, how much will you have in 45 years? How much would you have if all deposits were made on the FIRST of the year (as opposed to the last day of the year)? (please solve by hand and not excel)

Answer 1

If making deposits at the last day of the year:

For the next 45 years, you can save $4,000 per year; we can use FV of an Annuity formula to calculate the future value of after 45 years savings by you

FV = PMT *{(1+i) ^n−1} / i

Where,

Future value of annual savings FV =?

PMT = Annual savings = $4,000

n = N = number of deposits = 45 years

i = I/Y = interest rate per year = 8%

Therefore,

FV = $4,000 *{(1+8%) ^45−1} /8%

FV = $1,546,022.47

Therefore you will accumulate $1,546,022.47 in your retirement account after 45 years of deposits.

If making deposits at the first day of the year:

For the 45 years, you can save $4,000 per year; we can use FV of an Annuity due formula (as the deposits are made at the beginning of the year or first day of year) to calculate the future value of after 45 years savings by you

FV = PMT *(1+i) {(1+i) ^n−1} / i

Where,

Future value of annual savings FV =?

PMT = Annual savings = $4,000

n = N = number of deposits = 45 years

i = I/Y = interest rate per year = 8%

Therefore,

FV = $4,000 *(1+8%) {(1+8%) ^45−1} /8%

FV = $1,669,704.27

Therefore you will accumulate $1,669,704.27 in your retirement account after 45 years of deposits.