Question

John Rider wants to accumulate $95,000 to be used for his daughter's college education. He would like to have the amount available on December 31, 2026. 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 SD) (Use appropriate factor(s) from the tables provided.) Answer each of the following independent questions Required: 1. John were to deposit a single amount, how much would he have to invest on December 31, 2021? 2. If John were to make five equal deposits on each December 31, beginning a year later, on December 31, 2022, what is the required amount of each deposit? 3. If John were to make five equal deposits on each December 31, beginning now, on December 31, 2021, what is the required amount of each deposit? (For all requirements, Round your final answers to nearest whole dollar amount.) 1. Amount Annuity amount Annuity amount

Answer 1

1. Here we have to calculate present value. The future value is $95000. We will use the PV of $1 table with 8% interest rate and time period of 5 years (i.e. 2026 - 2021), as per below:

Present value = Future value * PVIF (8%, 5 years)

The value of PVIF(8%, 5 Years) from the PV of $1 table is 0.681.

Putting the values in the above formula, we get,

Present value = $95000 * 0.681

Present value = $64695

So, the amount he has to deposit is $64695

2. Here the deposits will be same every year, so it is an annuity. The future value of deposits is $95000. We will use the future value of annuity (FVA) of $1 for calculating the required deposits as below:

Future value = Annual deposits * FVA (8%, 5 Years)

The value of FVA (8%, 5 Years) from the FVA of $1 table is 5.8666.

Putting the values in the above formula, we get,

$95000 = Annual deposits * 5.8666

Annual deposits = $95000 / 5.8666

Annual deposits = $16193.36

So, annuity amount is $16193

3. Here the deposits will be same every year, so it is an annuity, and since the deposits are made immediately or at the beginning each year, so it is an annuity due. The future value of deposits is $95000. We will use the future value of annuity due (FVAD) of $1 for calculating the required deposits as below:

Future value = Annual deposits * FVAD (8%, 5 Years)

The value of FVAD (8%, 5 Years) from the FVAD of $1 table is 6.3359

Putting the values in the above formula, we get,

$95000 = Annual deposits * 6.3359

Annual deposits = $95000 / 6.3359

Annual deposits = $14993.92

So, annuity amount is $14994