Question

Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $62,000 cash immediately, (2) $19,000 cash immediately and a six-period annuity of $7,600 beginning one year from today, or (3) a six-period annuity of $12,500 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, 2030. Weimer will make annual deposits of $110,000 into a special bank account at the end of each of 10 years beginning December 31, 2021. 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, 2030?

Answer 1

Step-by-step explanation:

We must find the option with the greatest net present value (NPV).

1) The NPV is $62,000

2) First, you must calculate the NPV with the formula attached, for example:

NVP= ($7,600/(1+6%)^1)+($7,600/(1+6%^2)+($7,600/(1+6%^3)... and so on until year 6

With the excel formula "NPV" you can calculate the net present value specifying the interest rate, the cash flows.

NPV= $37,371.66

The TOTAL NPV= $19,000+$37,371.66= $56,371.66

3) NVP= ($12,500/(1+6%)^1)+($12,500/(1+6%^2)+($12,500/(1+6%^3)... and so on until year 6

NPV= $61,466.55

The best option is option 1.

Question 2.

We must use the compound interest formula:

Final Capital (FC)= Initial Capital (IC)*[(1+interest(i))]^(number of periods(n))

In Dec 31, 2022:

FC= $110,000*(1+7%)^1

FC=$117,000

Balance in Dec 31,2022 = $117,000+$110,000=$227,000

In Dec 31,2023

FC= $227,000*(1+7%)^1

FC= $243,639

Balance in Dec 31,2023= $243,639+$110,000= $353,639

And so on until 2030

If the Weimer corporation makes the last payment in 2030;

The balance in Dec,31 2030= $1,409,809+$110,000= $1,519,809