Question

John Rider wants to accumulate $65,000 to be used for his daughter’s college education. He would like to have the amount available on December 31, 2023. Assume that the funds will accumulate in a certificate of deposit paying 8% interest compounded annually. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Answer each of the following independent questions.

Required:
1. If John were to deposit a single amount, how much would he have to invest on December 31, 2018?
2. If John were to make five equal deposits on each December 31, beginning on December 31, 2019, what is the required amount of each deposit?
3. If John were to make five equal deposits on each December 31, beginning on December 31, 2018, what is the required amount of each deposit?
(For all requirements, Round your final answers to nearest whole dollar amount.)

	1. Amount 2. Annuity amount 3. Annuity amount

Answer 1

1)

Investment Required on December 31, 2018

$ 44,237.91

Working:

Present Value of Future Value

=

Future Value x Present Value of 1

=

$ 65,000.00

x

0.6806

=

$ 44,237.91

Present Value of 1

=

(1+i)^-n

Where,

=

(1+0.08)^-5

i

8%

=

0.6806

n

5

2)

Required amount of each deposit

$ 11,079.67

Working:

a.

Future Value of ordinary annuity of 1

=

(((1+i)^n)-1)/i

Where,

=

(((1+0.08)^5)-1)/0.08

i

8%

=

5.8666

n

5

b.

Annual deposit

=

Future Value / Future Value of annuity of 1

=

$ 65,000.00

/

5.8666

=

$ 11,079.67

When annual cash flow is occuerred at the end of each year, it is termed as ordinary annuity.

3)

Required amount of each deposit

$ 10,258.95

Working:

a.

Future Value of annuity due of 1

=

((((1+i)^n)-1)/i)*(1+i)

Where,

=

((((1+0.08)^5)-1)/0.08)*(1+0.08)

i

587%

=

6.3359

n

5

b.

Annual deposit

=

Future Value / Future Value of annuity of 1

=

$ 65,000.00

/

6.3359

=

$ 10,258.95

When annual cash flow is occuerred at the beginning of each year, it is termed as annuity due.