Homework Problems. What equal annual series of payments must be paid into a sink

Question

Homework Problems. What equal annual series of payments must be paid into a sinking fund in order to accumulate each given amount (a) $15,000 in 13 years at 5% compounded annually. (b) $20,000 in eight years at 6% compounded annually. (c) $5,000 in 25 years at 8% compounded annually. (d) $4,000 in eight years at 6.85% compounded annually. $847.5 $2,020 $68.5 391.98 Ans Bharath has borrowed $20,000 at an interest rate of 10% compounded annually. Equal payments will be made over a three-year period, with each payment made at the end of the corresponding year. What is the amount of the annual payment? What is the interest payment for the second year? Ans $8,042 & 1,39580

Explanation / Answer

1) a) Equal annual payment = y

y x (1 + 5%)12 + .... + y x (1 + 5%)0 = 15000

Solve for 'y': y = $846.84

Alternatively: y = pmt(5%,13,0,-15000) = $846.84

b) Similarly,

Equal annual payment = y

y x (1 + 6%)7 + .... + y x (1 + 6%)0 = 20000

Solve for 'y': y = $2020

y =  pmt(6%,8,0,-20000) = $2020

c)

y =  pmt(8%,25,0,-5000) = $68.4

d)

y =  pmt(6.85%,8,0,-4000) = $391.98

2)

PV = $20000, i = 10%

time period = 3 years

Annual payment = y

y/1.1 + y/1.12 + y/1.13 = 20000

y = $8042.3

Interest payment in 1st year = 10% x 20000 = $2000

Principal remaining at the end of 1st year = 20000 - (8042.3 - 2000) = $13957.7

Interest payment in 2nd year = 10% x 13957.7 = $1395.7 (= interest rate x principal at the end of 1st year)

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