A woman wishes to make a quarterly deposit into her savings account so that at t

Question

A woman wishes to make a quarterly deposit into her savings account so that at the end of 10 years the account balance will be $10,000. If the account e quarterly, how much should she deposit each quarter? annual interest, compounded The maintenance on a machine is expected to be $155 at the end of the first year, then increasing S35 each year for the next 7 years. What sum of money would need to be set aside now to pay the by maintenance for the 8-year period? Assume 6% interest. 3 Consider again the situation in Example Two(2). We wish to know the uniform annual equivalent maintenance cost. Compute an equivalent A for the maintenance costs

Explanation / Answer

(1)

Quarterly interest rate = 6% / 4 = 1.5%

Number of quarters = 10 x 4 = 40

Quarterly deposits ($) = Future value / FVIFA(1.5%, 40) = 10,000 / 54.2679** = 184.27

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

FVIFA(1.5%, 40) = [(1.015)40 - 1] / 0.015 = (1.8140 - 1) / 0.015 = 0.814 / 0.015 = 54.2679

(2)

Money to be set aside is the Present Worth of all costs, computed as follows.

PV Factor for year N = (1.06)-N

(3)

Uniform annual equivalent cost ($) = Present worth / PVIFA(6%, 8) = 1656.97 / 6.2098** = 266.83

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

PVIFA(6%, 8) = [1 - (1.06)-8] / 0.06 = (1 - 0.6274) / 0.06 = 0.3726 / 0.06 = 6.2098

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 Present Worth ($) = 1656.97

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