Question

# a) Consider a \$762 CF at the beginning of 2042. The interest rate is 2.8%. What...

a) Consider a \$762 CF at the beginning of 2042. The interest rate is 2.8%. What is the equivalent uniform amount for a series of end-of-year CFs spanning 2052-2056? (answer: \$218.05)

b)Consider a \$760 CF at the beginning of 2063. The interest rate is 3.9%. What is the equivalent uniform amount for a series of end-of-year CFs spanning 2050-2055? (answer: \$87.88)

How do you work this out my hand to get the answer?

a.) Future Value of \$762 at the beginning of the year 2052 = Present Value of annuity payment (2052-2056) at the beginning of the year 2052

• Future Value of \$762;

Number of years = 10

Interest Rate = 2.8%

Using TVM equation;

FV = PV (1+r)n

FV = 762(1.028)10 = \$1004.3524

• PV of annuity = \$1004.3524

Number of payments (n) = 5

Interest rate (r) = 2.8%

Let 'P' be the periodic payment

Then using PV of annuity formula

Solving for 'P', we get P = \$218.05

b.) PV of \$760 at the end of the year 2055 = FV of annuity payment (2050-2055) at the end of the year 2055

• PV of \$760;

Number of Periods (n) = 7

Interest rate = 3.9%

Using TVM equation;

PV = FV/(1+r)n

PV = 760/(1.039)7 = \$581.4398

• FV of annuity = \$581.4398

Number of payments (n) = 6

Interest Rate (r) = 3.9%

Let 'P' be the periodic payment.

Using FV of annuity formula;

Solving for 'P', we get P = \$87.88