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 $80,170 for a down payment on a small business. He will invest $34,000 today in a bank account paying 10% 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 $48,016. Payment was a noninterest-bearing note requiring Jasmine to make seven annual payments of $8,000 beginning one year from the date of purchase. What is the interest rate implicit in this agreement?
3. Sam Robinson borrowed $22,000 from a friend and promised to pay the loan in 12 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 an 11% annual rate. What is the annual payment Sam must make to pay back his friend?

Answer 1

Sol.1.

In this Question, time period- Number of years (n) has been asked. So, We will Solve the Problem for (n).

PV=$34,000, F.V=$80,170, r = 10% =0.1, n =?

P.V = P.V [P.V Factor for n, I =10%]

34,000 80,170 = [ P.V Factor for n, I=10%]

   0.4241 = P.V Factor for n= 9 years at I = 10%]    Note: From P.V $1 Table

Thus, In 9 years from now, $34,000 at 10% rate of interest will become $80170.

Q2. The Present Value annuity-PVA is $48,016. Jasmine Tea Company has to make 7 Annuity payment (A) of $8,000. The Time length (n) for payment is 7 years. The problem is solved for (i) rate of interest?

Annuity Factor = P.V.A Annuity amount

A.F = $48016 $8,000 = 6.002

The Present value of an ordinary annuity of $1 , where n= 4 years and i? [ from PVA of $1, = 4%].

Thus, the rate of interest is aproximatley 4% per annum.

Q3. The present value of loan (PVA) is $22,000, with 12 annual payment (A) and the rate (i) of interest is 11% per annum. We have to find out Annuity or Annual Payment.

Annuity Amount = PVA Annuity Factor

   = $22,000 6.4924

   = $3,388.58

   = $3,389

A.F: The Present value of an ordinary annuity of $ 1, where n= 12 years & i =11% per annum is =6.4924 from PVA of $1].

Thus, the annuity payment is $3,389.