Question & Answer: Kenworth Imaging got a $700,000 loan that came with a choice of two different repayments schedules. In Plan 1, the company would have to…..

Kenworth Imaging got a $700,000 loan that came with a choice of two different repayments schedules. In Plan 1, the company would have to repay the loan in 4 years with four equal payments at an interest rate of 10% per year. In plan 2, the company would repay the loan in 3 years, with each payment twice as large as the preceding one. How much larger in dollars was the final payment in Plan 2 that the final payment in Plan 1?

Expert Answer

Plan 1 ) Annual payment = loan amount / PVA 10%,4

= 700000/ 3.16987

= $ 220,829.25

Plan 2)Let the first payment be “X” .second payment will be 2x and third payment will be 2(2x) = 4x

Present value of loan = [PVF10%,1*CF1]+[PVF10%,2*CF2]+[PVF10%,3*CF3]

700000 = [.90909 * X]+[.82645*2X]+[.75131*4X]

700000 = .90909X+1.6529 X+3.00524

= 5.56723X

X (First payment): 700,000/5.56726

= 125,735.10

Last payment (4x) = 4*125735.10= $ 502,940.41

larger in dollars was the final payment in Plan 2 that the final payment in Plan 1 : 502940.41-220,829.25 = $ 282,111.16

**you can find the present value factors directly from table or using the formula 1/(1+i)^1

**for annuity factor it is 1/(1+i)^1+1/(1+i)^2+…1/(1+i)^4

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