Question

Problem 1-6 (LO1.3)

Using time value of money tables (Exhibit 1-A, Exhibit 1-B, Exhibit 1-C, Exhibit 1-D), calculate the following.    

a. The future value of $550 six years from now at 7 percent. (Round your FV factor to 3 decimal places and final answer to 2 decimal places.)

Future value            $ ____

b. The future value of $700 saved each year for 10 years at 8 percent. (Round your FV factor to 3 decimal places and final answer to 2 decimal places.)

Future value            $ ____

c. The amount a person would have to deposit today (present value) at a 5 percent interest rate to have $1,000 five years from now. (Round your PV factor to 3 decimal places and final answer to the nearest whole dollar.)

Deposit            $ ____

d. The amount a person would have to deposit today to be able to take out $500 a year for 10 years from an account earning 8 percent. (Round your PV factor to 3 decimal places and final answer to the nearest whole dollar.)

Deposit            $ ____

Answer 1

Part A:

Future Value:
FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$         550.00
Int Rate	7.0000%
Periods	6

Future Value = Present Value * ( 1 + r )^n
= $ 550 ( 1 + 0.07) ^ 6
= $ 550 ( 1.07 ^ 6)
= $ 550 * 1.5007
= $ 825.4
Part B:

FV of Annuity :
Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$         700.00
Int Rate	8.000%
Periods	10

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 700 * [ [ ( 1 + 0.08 ) ^ 10 ] - 1 ] / 0.08
= $ 700 * [ [ ( 1.08 ) ^ 10 ] - 1 ] / 0.08
= $ 700 * [ [2.1589] - 1 ] / 0.08
= $ 700 * [1.1589] /0.08
= $ 10140.59
Part C:Present Value:
PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Future Value	$              1,000.00
Int Rate	5.000%
Periods	5

Present Value = Future Value / ( 1 + r )^n
= $ 1000 / ( 1 + 0.05 ) ^ 5
= $ 1000 / ( 1.05 ) ^ 5
= $ 1000 / 1.2763
= $ 783.53
Part D:

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$               500.00
Int Rate	8.0000%
Periods	10

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 500 * [ 1 - [(1+0.08)^-10]] /0.08
= $ 500 * [ 1 - [(1.08)^-10]] /0.08
= $ 500 * [ 1 - [0.4632]] /0.08
= $ 500 * [0.5368]] /0.08
$3,355.04