When you were born, your dear old Aunt Minnie promised to deposit $1,000 in a savings
account for you on each and every one of your birthdays, beginning with your first. The
savings account bears a 5 percent compound annual rate of interest. You have just turned
25 and want all the cash. However, it turns out that dear old (forgetful) Aunt Minnie
made no deposits on your fifth, seventh, and eleventh birthdays. How much is in the
account now – on your twenty-fifth birthday?
Answers
Answer:
Explanation:
Solution:-
First Calculate the Future value of the entire annuity (FVIFA) and then subtract the future values of three individual missing payments.
Future value of Annuity for 25 years:-
Formula:-
FV = R
FV= Value of the annuity / Future Value of the annuity
R = Periodic payment amount
i/r = annual interest rate
n/t = number of period
FV of 5th deposit of $ 1,000 compounded for 25-5 = 20 years
FV of 7th deposit of $ 1,000 compounded for 25-7 = 18 years
FV of 11th deposit of $ 1,000 compounded for 25-11 = 14 years
FV = PV*(1+r)^n
PV = Present Value
i/r = annual interest rate
n/t = number of period
Calculation:-
FVIFA of 25 Deposits= R
R = $ 1,000
i = 5% = = 0.05
n = 25
=1,000
= 1,000
=1,000
= 1,000*(47.728)
= $ 47,728
FV of 5th deposit of $ 1,000 compounded for 25-5 = 20 years
FV = PV(1+r)^n
= 1,000(1+.05)20
= 1,000 (2.6533)
= $2,653.3
FV of 7th deposit of $ 1,000 compounded for 25-7 = 18 years
FV = PV(1+r)^n
= 1,000*(1+.05)^18
= 1,000 (2.4066)
= $2,406.6
FV of 11th deposit of $ 1,000 compounded for 25-11 = 14 years
FV = PV*(1+r)^n
= 1,000(1+.05)14
= 1,000 (1.9799)
= $1,979.9
Amount at the end of 25th Birthday
=$ 47,728 – $2,653.3 – $2,406.6 -$1,979.9
= $40,688.2
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