Question

Mary made five annual deposits of $8000 in a savings account that pays interest at a rate of 6% per year. One year after making the last deposit, the interest rate changed to 15% per year. Five years after the last deposit, how much accumulated money can she withdraw from the account?draw the cash flow diagram.

Answer 1

Answer-

Total annual payments = $ 8000 / year for 5 years
Interest rate = 6 %

year 1 = $ 8000
year 2 = $ 8000 x 1.06 + $ 8000 = $ 8480 + $ 8000 = $ 16480
year 3 = $ 16480 x 1.06 + $ 8000 = $ 17468.80 + $ 8000 = $ 25468.80
year 4 = $ 25468.80 x 1.06 + $ 8000 = $ 26996.93 + $ 8000 = $ 34996.93
year 5 = $ 34996.93 x 1.06 + $ 8000 = $ 37096.74 $ 8000 = $ 45096.74

Now the interest rate changed to 15 % per year

The amount after the last deposit = $ 45096.74

Amount after 5 years of last deposit = $ 45096.74 x 1.15⁵ = $ 45096.74 x 2.0113 = $ 90703.07

The amount that can be withdrawn after 5 years of last deposit = $ 90703.07

Time line is given below ( Cash flow diagram )

$ 8000 ------ $ 16480 --------- $ 25468.80 --------------- $ 34996.93 ------------- $ 45096.74 -------------- $ 90703.07

year 1-------- year 2------------ year 3------------------------ year 4------------------ year 5 -------------------- year 10