Question

Question 5

Your uncle offers to sell you his vintage Rolls Royce. He suggests a payment plan where you pay just $12,000 today, $7200 in 11 months and $70,000 in exactly 21 months from today. If the interest rate is 7.3% per annum compounding monthly, what is the value of the offer (in present day dollars, rounded to the nearest dollar; don’t show $ sign or commas)?

Answer 1

given interest rate = 7.3%

it is compounding monthly so monthly rate = 7.3 / 12 = 0.608333%

to calculate present value we should discount all cash flows at above rate of 0.608333%

Present value = cash flow / (1+ r)^n

where r = interest rate , n = time period

1st cash flow occur at time 0 so present value = 12000

2nd cash flow occur at 11 months from now so present value = 7200 / (1.00608333)^11 = 6735.33

3 rd cash flow occur at 21 months from now so present value = 70000 / (1.00608333)^21 = 61628.99

So the value of offer in present day dollars = 12000 + 6735.33 + 61628.99 = 80364.32 or 80364(rounded to nearest dollar)