Question

Geoffrey decides not to buy the car mentioned earlier. Instead, he is now considering a food delivery service "You, bars, meats" that his friend Gillian has recently started. Gillian has agreed that for a single payment of $66,000 today to help her launch her business, she will provide all the delivery services that Geoffrey needs for his business for the next 5 years. Geoffrey is considering borrowing the full amount from his business account.

Suppose that Geoffrey makes level quarterly repayments over the coming 5 years, the first payment being exactly 3 months from today. Again, the interest rate on Geoffrey's account is 4.1% p.a. effective.

(a) Calculate the size of the level quarterly repayment.

(b) How much money does Geoffrey owe on this loan after 1 year?

(c) How much interest does Geoffrey pay in the first year?

(d) Geoffrey believes that the overall benefit from this agreement amounts to $328.18083575068 per week in arrears (this would include money he would have spent on alternative delivery services, estimated additional profits from using Gillian's services, etc).

By considering only the initial cost of $66,000 and this weekly benefit of $328.18083575068, calculate the interest rate that represents the return on this investment, expressed as a nominal annual rate compounding weekly.

Answer 1

Part (a)

Rate per quarter = (1 + 4.1%)^1/4 - 1 = 1.0096%

The size of the level quarterly repayment

= PMT (Rate, Nper, PV, FV, Type)

= PMT (1.0096%, 4 x 5, -66000, 0, 0)

= $ 3,660.95

Part (b)

After 1 year, only 4 years will be remaining.

Amount outstanding after 1 year = -PV (Rate, Nper, PMT, FV) = - PV (1.0096%, 4 x 4, 3660.95, 0) = 53,838.94

Part (c)

Interest paid in the first year = interest paid in first 4 payments = -CUMIPMT(Rate, Nper, PV, Start, End, Type) = -CUMIPMT(1.0096%, 4*5, 66000,1,4,0) = 2,482.74

Part (d)

Hence, weekly interest rate = Rate (Nper, PMT, PV, FV) = Rate (5 x 52, 328.18083575068, -66000, 0) = 0.2062%

Hence, the interest rate that represents the return on this investment, expressed as a nominal annual rate compounding weekly = 0.2062% x 52 = 10.7200%