Question

1. Scott has saved $ 560 per quarter for the last three years in a savings account earning 5.2% compounded quarterly. He plans to leave the accumulated savings for seven years in the savings account at the same rate of interest. (i) How much will Scott have in total in his savings account?

2. What is the discounted value of payments of $ 60 made at the end of each month for nine years if interest is 4.5% compounded monthly?

Answer 1

1)

Amount saved = $560

Number of quarters amount saved = 3 x 4 = 12 quarters

Interest rate = 5.2%/4 = 1.3%

Future value at the end of 3 years =

$560/1.3% x [(1 + 0.013)^12 - 1]

= $43076.923 x [(1.013)^12 - 1]

= $43076.923 x [1.16765 - 1]

= $43076.923 x 0.16765 = $7221.846

Future value after 7 years =

$7221.846 x (1.013)^28

= $7221.846 x 1.4357

= $10368.4

2)

Amount made at the end of each month = $60

Maturity period = 9 x 12 = 108 months

Monthly interest rate = 4.5%/12 = 0.375%

Present value of payment at the end of each month =

$60 x Present value annuity factor (0.375%,108)

= $60 x 88.6714 = $5320.284