Question

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.

Please help answer both questions.

Answer 1

(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