Discounting and Present Value

EXERCISE 01

€10,000 is payable in nine months. Use a 7% annual interest rate for simple rational and compound discounting. For commercial discounting, use the discount rate equivalent to 7% interest over one year, d = 0.07/1.07; do not assume d = 7%.

A.Calculate present value under the three conventions.

A.

PV_{simple}=\frac{M}{1+it}

PV_{simple}=\frac{10{,}000}{1+0.07(9/12)}

€9,501.19

PV_{compound}=M(1+i)^{-t}

PV_{compound}=10{,}000(1.07)^{-9/12}

€9,505.22

d=\frac{i}{1+i},\qquad PV_{commercial}=M(1-dt)

d=\frac{0.07}{1.07}

PV_{commercial}=10{,}000\left(1-\frac{0.07}{1.07}\frac9{12}\right)

€9,509.35

Discounting and Present Value

EXERCISE 02

Current savings are $10,000. Additional savings of $9,000 arrive at the end of years 1 and 2. Tuition costs of $12,000 are paid at the end of years 2 and 3. The annual return is 7%.

A.How much can be spent on a holiday today?

A.

C_0=10{,}000+\frac{9{,}000}{1.07}+\frac{9{,}000-12{,}000}{1.07^2}-\frac{12{,}000}{1.07^3}

$5,995.32