Question

8. Keri was offered a choice of two payment options to settle her claims in a car accident case. The first option would pay her a single lump payment of 1,500,000 immediately, which she would deposit into an account earning an effective annual interest rate of i. The second option would pay her 4 annual payments of 300,000 with the first payment being made immediately and the final one at time 3. Keri can invest the payments from the second option into an account crediting an effective annual interest rate of 10% After 10 years, the account values of the two options are equal. Calculate i for the first option.

Answer 1

Value of receipts at the end of 3 years = 300,000(1+0.1)³ + 300,000(1.01)² + 300,000(1.01)+300,000

= $1,392,300

Value at the end of 10 years = $1,392,300*(1.1)⁷

= $2,713,198.82

According to questions, value at the end of 10 years under both the options is same

1,500,000(1+i)¹⁰ = 2,713,198.82

I = 6.11% (approx.)

10.Since the interest is re-invested in another account, value in first account will be equal to the principal value

Therefore, total value in first MSOE test account = $10,000*6 = $60,000

Value in second account will be as follows:

Year	Amount Invested	Closing Amount	Total Investment	Interest Earned @4%	Cumulative Ending Amount
1	500	-	500	20	520
2	1,000	520	1,520	60.8	1,580.8
3	1,500	1,580.8	3,080.8	123.23	3,204.03
4	2,000	3,204.03	5,204.03	208.16	5,412.19
5	2,500	5,412.19	7,912.19	316.49	8,228.68
6	3,000	8,228.68	11,228.68	449.15	11,677.83

Hence, amount in second account at the end of 6 years = $11,677.83