Question

1. What is the future value $490 per yearfor 8 years compounded annually at 10 percent?

2. Whats is the present value of $3,000 per year for 8 years discounted back to the present at 10 percent?

Answer 1

Solution:-

1) Calculation of future value of $490 per year for 8 years.

The FV can be calculated as follows:-

=CF1×(1+i)¹+ CF2×(1+i)²+ CF3×(1+i)³+ CF4×(1+i)⁴+ CF5×(1+i)⁵+ CF6×(1+i)⁶+ CF7×(1+i)⁷+ CF8×(1+i)⁸

Where CF= cash flow = $490 for all years

              i=interest rate = 10%

=490×(1.10)¹+490×(1.10)²+490×(1.10)³+490×(1.10)⁴+490×(1.10)⁵+490×(1.10)⁶+490×(1.10)⁷+490×(1.10)⁸

=539+592.9+652.19+717.41+789.15+868.06+954.87+1050.36

=$6,163.94

Hence the future value= $6,163.94

Note:- since nothing is said about the deposit, we assume the deposit is at the beginning of the year.

2) Calculation of the present value

The PV of can be calculated as follows:-

=CF1/(1+i)¹+ CF2/(1+i)²+ CF3/(1+i)³+ CF4/(1+i)⁴+ CF5/(1+i)⁵+ CF6/(1+i)⁶+ CF7/(1+i)⁷+ CF8/(1+i)⁸

=3000/(1.10)¹+3000/(1.10)²+3000/(1.10)³+3000/(1.10)⁴+3000/(1.10)⁵+3000/(1.10)⁶+3000/(1.10)⁷+3000/(1.10)⁸

=2727.27+2479.33+2253.94+2049.04+1862.76+1693.42+1539.47+1399.52

=$16,004.79

Note:- Since nothing is said the amount of cash flow is assumed at the end of the year.

Hence the present value = $16,004.79

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