Question

The following situations should be considered independently. (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.)

1. John Jamison wants to accumulate $69,739 for a down payment on a small business. He will invest $35,000 today in a bank account paying 9% interest compounded annually. Approximately how long will it take John to reach his goal?
2. The Jasmine Tea Company purchased merchandise from a supplier for $38,779. Payment was a noninterest-bearing note requiring Jasmine to make eight annual payments of $6,000 beginning one year from the date of purchase. What is the interest rate implicit in this agreement?
3. Sam Robinson borrowed $20,000 from a friend and promised to pay the loan in 15 equal annual installments beginning one year from the date of the loan. Sam’s friend would like to be reimbursed for the time value of money at a 10% annual rate. What is the annual payment Sam must make to pay back his friend?

John Jamison wants to accumulate $69,739 for a down payment on a small business. He will invest $35,000 today in a bank account paying 9% interest compounded annually. Approximately how long will it take John to reach his goal? (Do not round intermediate calculations. Round the value of "n" to the nearest whole number.)

Present Value:
n =
i =
Future Value

The Jasmine Tea Company purchased merchandise from a supplier for $38,779. Payment was a noninterest-bearing note requiring Jasmine to make eight annual payments of $6,000 beginning one year from the date of purchase. What is the interest rate implicit in this agreement? (Do not round intermediate calculations. Round the interest rate to 1 decimal place.)

Present Value:
n =
i =
Annuity Payment

Sam Robinson borrowed $20,000 from a friend and promised to pay the loan in 15 equal annual installments beginning one year from the date of the loan. Sam’s friend would like to be reimbursed for the time value of money at a 10% annual rate. What is the annual payment Sam must make to pay back his friend? (Do not round intermediate calculations. Round your final answers to nearest whole dollar amount.)

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Table or calculator function:
Present Value:
n =
i =
Annual Installment:

Answer 1

Solution 1:

Amount invested = $35,000

Interest rate = 9%

Desired future value = $69,739

Let time required = n

$35,000 (1+0.09)^n = $69,739

= (1.09)^n = 1.9925

Refer CI table, this factor falls at n= 8

Therefore it will take 8 years to reach the goal.

Solution 2:

Present value of annual payments = $38,779

Annual installment = $6,000

Period = 8 years

Let implicit rate = i

Now

$6,000 * Cumulative PV Factor at i for 8 periods = $38,779

Cumulative PV Factor at i for 8 periods = 6.46317

Refer PV Factor table, this factor falls at i = 5%

Solution 3:

Amount borrowed = $20,000

Interest rate = 10%

Nos of periods = 15

Annual installment = $20,000 / Cumulative PV factor at 10% for 15 periods

= $20,000 / 7.60608 = $2,629