Question

Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $80,000 cash immediately, (2) $29,000 cash immediately and a six-period annuity of $8,700 beginning one year from today, or (3) a six-period annuity of $16,200 beginning one year from today. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)1. Assuming an interest rate of 6%, determine the present value for the above options. Which option should Alex choose?2. The Weimer Corporation wants to accumulate a sum of money to repay certain debts due on December 31, 2027. Weimer will make annual deposits of $155,000 into a special bank account at the end of each of 10 years beginning December 31, 2018. Assuming that the bank account pays 7% interest compounded annually, what will be the fund balance after the last payment is made on December 31, 2027?

Answer 1

To find the present value of each option, we need to use the present value of a lump sum formula and the present value of an annuity formula. The formulas are:

PV=F×(1+i)n1​

PVA=PMT×i1−(1+i)n1​​

Where PV is the present value, F is the future value, i is the interest rate per period, n is the number of periods, PVA is the present value of an annuity, and PMT is the payment amount per period.

Using these formulas, we can calculate the present value of each option as follows:

Option 1: $80,000 cash immediately

PV = $80,000

Option 2: $29,000 cash immediately and a six-period annuity of $8,700 beginning one year from today

PV = $29,000 + PVA

PVA = 8,700x\frac{1 - \frac{1}{(1 + 0.06)^6}}{0.06}$

PVA = 8,700x4.9173

PVA = 42,780.51

PV = $29,000 + 42,780.51

PV = 71,780.51

Option 3: a six-period annuity of $16,200 beginning one year from today

PV = PVA

PVA = 16,200x\frac{1 - \frac{1}{(1 + 0.06)^6}}{0.06}$

PVA = 16,200x4.9173

PVA = 79,640.26

Based on these calculations, Alex should choose option 3 as it has the highest present value.

To find the fund balance after the last payment is made on December 31, 2027, we need to use the future value of an annuity formula. The formula is:

FVA=PMT×i(1+i)n−1​

Where FVA is the future value of an annuity, PMT is the payment amount per period, i is the interest rate per period, and n is the number of periods.

Using this formula, we can calculate the fund balance as follows:

FVA = 155,000x\frac{(1 + 0.07)^{10} - 1}{0.07}$

FVA = 155,000x13.8164

FVA = 2,141,542

Therefore, the fund balance after the last payment is made on December 31, 2027 will be $2,141,542.

Answer 2

Step-by-step explanation:

To determine the present value of each option, we can use the following formulas:

Option 1: PV = $80,000 Option 2: PV = $29,000 + (PVA 6, 6%)$8,700 Option 3: PV = (PVA 6, 6%)$16,200

Using the PV of an annuity table (Table 2), we can find that the present value factor for a six-period annuity at 6% is 4.1118.

Option 2: PV = $29,000 + (4.1118)$8,700 = $65,859.46 Option 3: PV = (4.1118)$16,200 = $66,479.56

Therefore, the present value of Option 1 is $80,000, the present value of Option 2 is $65,859.46, and the present value of Option 3 is $66,479.56.

Based on these calculations, Alex should choose Option 1 as it has the highest present value.

We can use the formula for the future value of an annuity (FVA) to determine the fund balance after the last payment is made:

FV = C * ((1 + r)^n - 1)/r

Where: C = annual deposit r = interest rate n = number of periods

In this case, C = $155,000, r = 7%, and n = 10. We can calculate the future value of the annuity as follows:

FV = $155,000 * ((1 + 0.07)^10 - 1)/0.07 = $2,468,355.12

Therefore, the fund balance after the last payment is made on December 31, 2027 will be $2,468,355.12.