Question

PLEASE SHOW ALL WORK.

2. A bank is negotiating a loan. The loan can either be paid off as a lump sum of $100,000 at the end of five years, or as equal annual payments at the end of each of the next five years. If the interest rate on the loan is 10% regardless of the payment method, what annual payments should be made so that both forms of payment are equivalent? 3. You have an investment opportunity that requires an initial investment of $5000 today and will pay $6000 in one year. What is the annual rate of return of this opportunity

3. You have an investment opportunity that requires an initial investment of $5000 today and will pay $6000 in one year. What is the annual rate of return of this opportunity?

4. A businessman wants to buy a truck. The dealer offers to sell the truck for either $120,000 now, or six yearly payments of $25,000, with the first payment one year after the purchase of the truck. What is the yearly interest rate being offered by the dealer (to the customer)?

Answer 1

(2)

Option 1 --> Payment at end of 5 years = $100000

=> FV of the loan is $100000

Option 2 --> Let annual payments be P (at interest rate r = 10% or 0.10)

FV of the payments made = P(1+r)⁴ + P(1+r)³ + P(1+r)² + P(1+r) + P = P[(1+r)ⁿ -1]/r = 6.1051P

This is equal to FV of the first option

=> 6.1051P = 100000 => P = 16379.75

Hence, annual payment of $16379.75 should be made

(3) Given, Initial Investment = PV = $5000

Value of investment after 1 year = FV = $6000

Let rate of return be r

=> FV = PV(1+r)ⁿ

=> 6000 = 5000(1+r)

=> r = 0.20 or 20%

(4) Present Value PV of the truck = $120000

Yearly Payments P = $25000

Let annual interest rate be r

number of payments = n = 6

=> NPV of yearly payments = P/(1+r) + P/(1+r)² + ... + P/(1+r)⁶ = P[1- (1+r)^-n]/r = 25000[1- (1+r)^-6]/r

This is equal to PV of $120000

=> 120000 = 25000[1- (1+r)^-6]/r

=> 4.8r = 1 - (1+r)^-6

=> r = 0.0675 or 6.75%