7 What is the annual sinking fund payment if in 10 years you

7. What is the annual sinking fund payment if in 10 years you need to have $200,000 available for equipment replacement. Use an interest rate o f5% compounded semiannually. 8. What is the present value of 25 years of equal quarterly payments of $2,500 at an interest rate of 4% compounded quarterly?

Solution

7. Formula for calculating monthly payment to achieve a Future Value: (Sinking Fund)

PMT = (FV*r)/[(1+r)^n – 1]

[Where PMT is the periodic payment, FV is the future value, r is the rate of interest, and n is the number of periods of payment]

FV = $200,000. Interest = 5% compounded annually (0.05). Term = 10 years.

PMT = ($200,000*0.05)/[(1+0.05)^10 – 1]

PMT = 10,000/(1.6288 – 1)

PMT = 10,000/0.6288

PMT = 15,903.30.             

[FV = 15,903.30(0.6288/0.05). FV = 15,903.30*12.576 = $1,999,999.90.].

8. The present value (PV) of an annuity of n payments of R dollars with interest compounded at a rate of i. per period:

PV = R[1 – (1+i)^-n/i]

[Here, i is = 4%/4 = 0.04/4 = 0.01 and n = 4x25 = 100.]

PV = $2,500[(1 – (1+0.01)^-100)/0.01]

PV = $2,500[(1 – 0.3697)/0.01]                                                    [0.6303/0.01 = 63.03]

PV = $2,500*63.03

PV = $157,575.

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