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Jody wants to save for her college expenses. She received a$6,000 gift from her grandparents...

Jody wants to save for her college expenses. She received a $6,000 gift from her grandparents at age 10 and wants to see it increase to $9,000 by the time she turns 15. If she invests all of her gift, what rate of return should be expected to reach her goal of $9,000? For 5 extra credit points, instead of a $6,000 gift, 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

Calculating Rate of Interest and Present Value of Annuity

a.)Future Value of Single Payment =>

FV_n = PV(1+r)ⁿ

9000 = 6000(1+r)⁵

1.5 = (1+r)⁵

1.5^1/5 = 1+r

r = 1.084475-1

r = 8.4475%

Please note that r can be calculated with Trial and Error method.

b.) Present Value of a Growth Annuity=>

Formula =

=

= 5064.48

Here: P - Annual Payment

r - rate of interest

g - growth rate

n - number of period

jeff jeffy answered 2 years ago

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