1. John Jamison wants to accumulate $77,709 for a down payment on a small business. He will invest $39,000 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 $45,102. Payment was a noninterest-bearing note requiring Jasmine to make five annual payments of $11,000 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 10 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?

Question

Business

Rodolfo Nash

4 March, 05:53

1. John Jamison wants to accumulate $77,709 for a down payment on a small business. He will invest $39,000 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 $45,102. Payment was a noninterest-bearing note requiring Jasmine to make five annual payments of $11,000 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 10 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?

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Answers (1)

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Julie Harvey · Answer 1

Instructions are listed below

Explanation:

Giving the following information:

1. John Jamison wants to accumulate $77,709 for a down payment on a small business. He will invest $39,000 today in a bank account paying 9% interest compounded annually.

We need to find how many years will it take to reach the objective.

Using the final value formula:

FV = PV * (1+i) ^n

We isolate n:

n=[ln (FV/PV) ]/ln (1+i)

n = ln (77709/39000) / ln (1+0.09)

n = 8 years

2) The Jasmine Tea Company purchased merchandise from a supplier for $45,102. Payment was a noninterest-bearing note requiring Jasmine to make five annual payments of $11,000 beginning one year from the date of purchase.

Implicit interest = [11000 / (45102/5) ]-1

Implicit interest = 0.2195 = 21.95% annual

3) Sam Robinson borrowed $20,000 from a friend and promised to pay the loan in 10 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.

We need to find the annual payment:

First, we need to find the final value of the loan:

FV = PV * (1+i) ^n

FV = 20000 * (1.10^10) = $51.875

Now, we cancalculate the annual payment:

Using the following formula:

FV = {A*[ (1+i) ^n-1]}/i

A = annual payment

Isolating A:

A = (FV*i) / [ (1+i) ^n-1]

A = (51875*0.10) / (1.10^10-1)

A=$3254.917