Question

Find the amount accumulated FV in the sinking fund. HINT [See Example 1.] (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.)

$400 is deposited monthly for 10 years at 2% per year in an account containing $6,000 at the start

FV = $

Find the periodic payments PMT necessary to accumulate the amount given in a sinking fund. HINT [See Example 2.] (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.)

$10,000 in a fund paying 5% per year, with monthly payments for 5 years

PMT = $

Find the periodic payments PMT necessary to accumulate the amount given in a sinking fund. HINT [See Example 2.] (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.)

$20,000 in a fund paying 7% per year, with quarterly payments for 20 years

PMT = $

Answer 1

solution 1:

Period = 10 years, 120 monthly periods

Interest rate =2%, 0.16666% monthly rate

Furtuer value = $6,000 * FV factor at 0.166666% for 120th period + $400 * Cumulative FV factor at 0.1666666% for 120 periods of ordinary annnuity

= $6,000 * 1.221199 + $400*132.71966

= $60,415.06

Solution 2:

Future value = $10,000

Let monthly payment = X

Total monthly period = 5*12 = 60 periods

Rate of interest = 5% / 12 = 0.41666666%

X * Cumulative FV factor at 0.41666666% for 60 periods = $10,000

X * 68.00608 = $10,000

X = $147.05

Solution 3:

Future value = $20,000

Let quarterly payment = X

Total quarterly periods = 20*4 = 80 periods

Interest rate = 7%/4 = 1.75% per quarter

X * Cumulative FV Factor at 1.75% for 80 periods = $20,000

X * 171.79382 = $20,000

X = $116.42

Let