Question

A lottery winner will receive $2 million at the end of each of the next fourteen years. What is the future value​ (FV) of her winnings at the time of her final​ payment, given that the interest rate is 8.2​% per​ year?

A. $78.61 million

B. $49.13  million

C.$68.78million

D. $39.30 million

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. Which of the following is closest to the interest rate being offered by the​ dealer?

A. 7.8​%

B. 5.8​%

C.6.8​%

D. 9.8​%

Answer 1

Question 1 - Option B 49.13 million

Future Value at the end of 14th Year = Annual Payment * Future Value Annuity Factor 8.2%, 14 Years

Future Value = 2 * 24.56 = 49.128 million

Alternatively it can also be calculated as using table as shown below

Year	Compounded for (Years)	Cash Flow	Future Value @8.2%
1	13	2	5.57
2	12	2	5.15
3	11	2	4.76
4	10	2	4.40
5	9	2	4.07
6	8	2	3.76
7	7	2	3.47
8	6	2	3.21
9	5	2	2.97
10	4	2	2.74
11	3	2	2.53
12	2	2	2.34
13	1	2	2.16
14	0	2	2.00
			49.12

Question 2 - Option C 6.8%

This question is to be calcualted using IRR formulae,

IRR is the discount rate at which present value of all the cash flows is equal to initial investment

we will consider the price of truck of 120000 to be the initial outflow at year 0, and find out the discount rate at which 25000 payment for 6 years will be equal to 120000 using IRR formulae in excel

Year	Cash Flow
0	-120000
1	25000
2	25000
3	25000
4	25000
5	25000
6	25000
IRR	6.77%