Question

# 1. John wishes to make a quarterly deposit into his savings account so that at the...

1. John wishes to make a quarterly deposit into his savings account so that at the end of 10 years the account balance will be \$10,000. If the account earns 6% annual interest, compounded quarterly, how much should he deposit each quarter?

2. The maintenance on a machine is expected to be \$155 at the end of the first year, then increasing by \$35 each year for the next 7 years. What sum of money would need to be set aside now to pay the maintenance for the 8-year period? Assume 6% interest.

(1)

Quarterly interest rate = 6% / 4 = 1.5%

Number of quarters = 4 x 10 = 40

Quarterly deposit (\$) = 10,000 / F/A(1.5%, 40) = 10,000 / 54.2679** = 184.27

**F/A(r%, N) = [(1 + r)N - 1] / r

F/A(1.5%, 40) = [(1.015)40 - 1] / 0.015 = (1.8140 - 1) / 0.015 = 0.8140 / 0.015 = 54.2679

(2)

Money to be set aside now is equal to the Present Worth (PW) of the costs, computed as follows.

PV factor for year N = (1.06)-N

 Year Cost (\$) PV Factor @6% Discounted Cost (\$) (A) (B) (A) x (B) 1 155 0.9434 146.23 2 190 0.8900 169.10 3 225 0.8396 188.91 4 260 0.7921 205.94 5 295 0.7473 220.44 6 330 0.7050 232.64 7 365 0.6651 242.75 8 400 0.6274 250.96 PW of Costs (\$) = 1,656.97

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