Question

For each of the following situations, identify (1) the case as either (a) a present or a future value and (b) a single amount or an annuity, (2) the table you would use in your computations (but do not solve the problem), and (3) the interest rate and time periods you would use. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.) a. You need to accumulate $10,000 for a trip you wish to take in four years. You are able to earn 8% compounded semiannually on your savings. You plan to make only one deposit and let the money accumulate for four years. How would you determine the amount of the one-time deposit? b. Assume the same facts as in part (a) except that you will make semiannual deposits to your savings account. What is the required amount of each semiannual deposit? (Round your answer to 2 decimal places.) c-1. You want to retire after working 40 years with savings in excess of $1,000,000. You expect to save $4,000 a year for 40 years and earn an annual rate of interest of 8%. Will you be able to retire with more than $1,000,000 in 40 years?

Answer 1

Answer:

a. The present value of a future value of $10,000 is $7,310.

b. The present value of an annuity for a future value of $10,000 is $1,043.54.

c. Yes, you will retire with $1,036,226.07 .

Explanation:

a) Data and Calculations:

Future value = $10,000

Interest - 8% compounded semiannually

Period of investment = 4 years

Using the present value table, the discount factor of 0.731, the future value of $10,000 is $7,310

b) You will need to contribute $1,043.54 at the beginning of each period to reach the future value of $10,000.00.

FV (Future Value) $10,000

PV (Present Value) $7,306.90

N (Number of Periods) 8.000

I/Y (Interest Rate) 4.000%

PMT (Periodic Payment) $1,043.54

Starting Investment $0.00

Total Principal $8,348.30

Total Interest $1,651.70

c)  $1,000,000 in 40 years:

FV (Future Value) $1,036,226.07

PV (Present Value) $47,698.45

N (Number of Periods) 40.000

I/Y (Interest Rate) 8.000%

PMT (Periodic Payment) $4,000.00

Starting Investment $0.00

Total Principal $160,000.00

Total Interest $876,226.07