Question

Find the future or compound value of a $250, five-year ordinary annuity at 8 percent annual interest if the payment at the end of year 3 is omitted. 250 250 0 250 250 |____________|___________|__________|___________|__________| t0 t3 t5

Answer 1

Answer:

$1,269.05

Explanation:

An ordinary annuity is an annuity that is payment can is made at the end of each period.

For each period, the future value (FV) can be calculated as follows:

FV = P × (1 + r)^n ........................... (1)

Where P = amount of payment

r = periodic interest interest rate

n = period in reference

From the calculation, FV for each year can be calculated using equation (1) as follows:

Year 1 FV:

P = $250

r = 8% = 0.08

n = 1

FV = $250 × (1 + 0.08)^1 = $250 × 1.0800  = $270.00

Year 2 FV:

P = $250

r = 8% = 0.08

n = 2

FV = $250 × (1 + 0.08)^2 = $250 ×  1.1664  = $291.60

Year 3 FV:

This is equal to zero because it is omitted.

Year 4 FV:

P = $250

r = 8% = 0.08

n = 4

FV = $250 × (1 + 0.08)^4 = $250 × 1.3605  = $340.12

Year 5 FV:

P = $250

r = 8% = 0.08

n = 5

FV = $250 × (1 + 0.08)^5 = $250 × 1.4693  = $367.33

FV for 5 years = $270.00 + $291.60 + 0 + $340.12 + $367.33 = $1,269.05

Therefore, the future or compound value of a $250, five-year ordinary annuity at 8 percent annual interest if the payment at the end of year 3 is omitted is $1,269.05.