Question

Compute the present value of a $5,500 deposit in year 1, and another $5,000 deposit at the end of year 4 using an 8 percent interest rate. (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Answer 1

Step-by-step explanation:

Present value is the value in the present of a sum of money, in contrast to some future value it will have when it has been invested at compound interest.

It can be calculated using future value formula below

A = P(1+r/100)^n

where

A = Future value

P = Present value

r = Rate of interest

n = time period

Present Value = Value at Year 1 + Value at Year 4

Calculating Value at Year 1

A = $5,500

r = 8%

n = 1

From A = P(1+r/100)^n ; Make P the subject of formula

P = A ÷ (1 + r/100)^n

Substitute in values

P = $5,500 ÷ (1 + 8/100)^1

P = $5,500 ÷ (1 + 0.08)

P = $5,500/1.08

P = $5092.5925926

P = $5092.59 ----

Present Value at Year 1 = $5092.59

Calculating Value at Year 4

A = $5,000

r = 8%

n = 1

From A = P(1+r/100)^n ; Make P the subject of formula

P = A ÷ (1 + r/100)^n

Substitute in values

P = $5,000 ÷ (1 + 8/100)⁴

P = $5,000 ÷ (1 + 0.08)⁴

P = $5,000/1.08⁴

P = $3675.149263982267

P = $3675.15 ----

Present Value at Year 4 = $3675.15

Present Value = Value at Year 1 + Value at Year 4

Substitute each value

Present Value = $5092.59 + $3675.15

Present Value = $8,767.74