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 $75,000 for a down payment on a small business. He will invest $35,000 today in a bank account paying 8% interest compounded annually. Approximately how long will it take John to reach his goal?PV= $35,000, n=?, i=8%, FV=$75,0002. The Jasmine Tea Company purchased merchandise from a supplier for $43,700. Payment was a noninterest-bearing note requiring Jasmine to make six annual payments of $8,000 beginning one year from the date of purchase. What is the interest rate implicit in this agreement?PV=$43,700, n=6, i=%, Annuity Payment= $8,0003. Sam Robinson borrowed $18,000 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 9% annual rate. What is the annual payment Sam must make to pay back his friend?Table or calculator function: PVA of $1. PV= $18,000, n=10, i=9%, Annual Installment=?

Answer 1

Answer:

Explanation:

(1)

FV = PV x (1 + r)^N  

FV = $75,000

PV = $35,000

r = 8%

75,000 = 35,000 x (1.08)^N

(1.08)N = 2.1429

N ln 1.08 = ln 2.1429

N = ln 2.1429 / ln 1.08 = 0.33 / 0.033 = 10 years

(2)

FV = Annual payment, A x PVA

FV = $43,700

n = 6 years

A = 8,000

43,700 = 8,000 x PVA

PVA = 5.4625

PVIFA (6 years, r%) = 5.4172

r=3%.

(3)

PV = Annual payment, A x PVIFA (r%, n years)

PV = $18,000

n = 6 years

r = 9%

$18,000 = A x PVIFA (9%, 6 years) = A x 4.4859 [From PVIFA table]

A = $18,000 / 4.4859 = $4,012.57