Suppose you saved $483 at the end of each month for 37 years and your savings...

Suppose you saved $483 at the end of each month for 37 years and your savings earned an interest rate of 3.5%. If instead you had saved for only 11 years, how much would you have had to save each month in order to reach the same final balance? Round to the nearest cent.

Solutions

Expert Solution

Answer:

Part 1

PMT (per month deposit) = $483

no of year = 37 years

n = 37 x 12 = 444

Rate = 3.5% per year

rate per month = 3.5% / 12 = .29167%

Future value = PMT[(1+R)^n -1/R]

= 483 [ (1.0029167)^444 - 1/.29167%]

= 483[(3.644120775) -1 / .29167%]

= 483[ 2.644120775/ .29167%]

= 483 X 906.5556944

= $437,866.40

Part B

Future value = = $437,866.40

period = 11 years

n = 11 x 12 = 132

Rate = 3.5% per year

rate per month = 3.5% / 12 = .29167%

Monthly deposit = Future value /[(1+R)^n -1/R]

= 437,866.40 / [ (1+ .29167%)^132 - 1/.29167%]

= 437,866.40 / [ (1.0029167%)^132 - 1/.29167%]

= 437,866.40 / [1.468791026 - 1/.29167%]

= 437,866.40 / [.468791026/.29167%]

= 437,866.40 / 160.7283517

= $2724.26 per month

jeff jeffy answered 2 years ago

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