Question

You have just won the lottery! You can either receive $183,555 per year for 20 years or $2,300,000 as a lump sum payment today. What is the interest rate on the annuity option?

A. 4.25 percent
B. 5.50 percent
C. 4.94 percent
D. 4.75 percent
E. 3.98 percemt

Answer 1

Option C is the correct option.

C. 4.94 percent

Step-by-step explanation:

The interest rate on the annuity option is determined through the concept of present value, comparing the annuity payments to the lump sum amount.

The present value formula for an annuity is used to calculate the interest rate. In this case, the choice is between receiving $183,555 annually for 20 years or a lump sum of $2,300,000 today.

To calculate the interest rate, we employ the present value of an annuity formula:

`\[PV = (PMT * (1 - (1 + r)^(-n)))/(r),\]`

where:

- \(PV\) is the present value of the annuity,

- \(PMT\) is the annuity payment per period,

- \(r\) is the interest rate per period,

- \(n\) is the total number of periods.

The lump sum payment is already the present value, and the annuity payment is \(PMT = $183,555\), and \(n = 20\) years.

By rearranging the formula and solving for \(r\), the interest rate is found to be approximately 4.94 percent.

This rate makes the present value of the annuity payments equivalent to the lump sum amount, providing an equal value for either option.

Therefore, option C, 4.94 percent, is the correct interest rate for the annuity option.