Question

1. In 7 years I aim to have 40,000 saved, I earn 8% compounded annually
   1. If I start saving today, how much would I need to save each year? (making 7 equal annual payments)
   2. If I start saving in a year, how much would I need to save each year? (making 7 equal annual payments)

Please show work in excel.

Answer 1

We can use Future value (FV) of annuity due formula to calculate annual deposits (Future value of annuity due formula as the deposits are at the beginning of each year)

FV = PMT*(1+i) *{(1+i) ^n−1} / i

Where FV =$40,000

PMT = Annual savings =?

n = N = number of payments = 7 (year)

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

Therefore,

$40,000 = Annual savings *(1+8%) *{(1+8%) ^7−1} / 8%

Annual savings = $4,150.83

Therefore you have to save $4,150.83 each year for 7 years.

Now we can use FV of an ordinary annuity formula to calculate the annual savings by you (ordinary annuity formula as the deposits are at the end of year)

FV = PMT *{(1+i) ^n−1} / i

Where,

Future value of annual savings FV = $40,000

PMT = Annual savings =?

n = N = number of payments = 7 (years)

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

Therefore,

$40,000 = Annual savings *{(1+8%) ^7−1} /8%

Annual savings = $4,482.90

Therefore you have to save $4,482.90 each year for 7 years.