Jody's grandparents deposited $1,200 annually to a savings account and increased the deposits at a rate...

Jody's grandparents deposited $1,200 annually to a savings account and increased the deposits at a rate of 3% annually for 5 years. What is the present value of this investment earning 8% annually?

Expert Solution

There is a growing annuity.

Given,

First deposit = F = 1,200

Rate = r = 8% = 8/100 = 0.08

Number of year = n = 5

Rate of growing = g = 3% = 3/100 = 0.03

Present value = P =?

The formula is as below:

P = [F/(r – g)] [1 – {(1 + g) / (1 + r)}^n]

= [1200/(0.08 – 0.03)] [1 – {(1 + 0.03) / (1 + 0.08)}^5]

= [1200 / 0.05] [1 – (1.03/1.08)^5]

= 24,000 × [1 – 0.953703^5]

= 24,000 × [1 – 0.788979]

= 24,000 × 0.211021

= 5,064.50 (Answer)

jeff jeffy answered 2 years ago

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