Question

7. Today you inherit an account with a balance of $5400. For a while you don't do anything with the account but it continues to accrue interest. Exactly 21 months from today you start an ambitious savings plan and deposit $190 into the account. You plan to deposit that much each month. Exactly 45 months from today you reconsider your plan, make your last deposit, and make no additional deposits. You nonetheless leave the account alone and it continues to accrue interest at a rate of 7.5% compounded monthly. You finally close the account exactly 6 years from today, 1. Construct timelines 2. Find account balance int = 21 3. Find account balance int = 45. 4 Find account balance int = 72

Answer 1

Hi

Please refer to the image attached

Some rows have been hidden to avoid repetition.

It is assumed that the deposits are made at the beginning of the month. Answer may change if it is assumed at the end of the month.

1 2 20 A B C Month Opening bal. Deposit 1 $ 5,400.00 $ - $5,433.75 $ - $ 6,078.63 $ - $ 6,116.62 $ 190.00 $ 6,346.04 $ 190.00 $11,772.34 $ 190.00 $12,037.11 $ 190.00 $12,303.53 $ $14,377.29 $ - $14,467.14 $ - D E Int. @7.5% Closing Bal. $ 33.75 $ 5,433.75 $ 33.96 $5,467.71 $ 37.99 $ 6,116.62 $ 39.42 $ 6,346.04 $ 40.85 $ 6,576.89 $ 74.76 $12,037.11 $ 76.42 $12,303.53 $ 76.90 $12,380.42 $ 89.86 $14,467.14 $ 90.42 $14,557.56 23 22

With formulae-

A B C D 1 Month Opening bal. Deposit Int. @ 7.5% Closing Bal. 21 5400 =(B2+C2)*7.5%/12 =B2+C2+D2 3 =A2+1 =E2 0 =(B3+C3)*7.5%/12 =B3+C3+D3 21 =A20+1 =E20 =(B21+C21)*7.5%/12 =B21+C21+D21 22 =A21+1 =E21 190 =(B22+C22)* 7.5%/12 =B22+C22+D22 23 =A22+1 =E22 190 =(B23+C23)*7.5%/12 =B23+C23+D23 45 =A44+1 =E44 = (B45+C45)*7.5%/12 =B45+C45+D45 46 =A45+1 =E45 =(B46+C46)*7.5%/12 =B46+C46+D46 47 =A46+1 =E46 =(B47+C47)*7.5%/12 =B47+C47+D47 72 =A71+1 =E71 =(B72+C72) *7.5%/12 =B72+C72+D72 73 EA 72+1 =E72 =(B73+C73) *7.5%/12 =B73+C73+D73 190 190 IBA 0 74