Question

Jane has been offered a choice between a lump sum payment of $100,000 today or an annuity that pays $8,000 per year for 20 years, starting one year from today. If the interest rate is 6% per year, which option should she choose?

Answer 1

Jane must calculate the present value of the $8,000 annual annuity using the present value of an ordinary annuity formula to compare it with the $100,000 lump sum. The importance of compound interest is illustrated by how a $3,000 investment grows over 40 years at a 7% annual rate of return.

Step-by-step explanation:

To determine which option Jane should choose, we can compare the present value of the annuity to the lump sum amount. The present value of an annuity formula is given by:

PV = C x ( {(1 - (1 + r)^{-n})} / {r} )

where:

- PV is the present value of the annuity,

- C is the annual payment,

- r is the interest rate per period, and

- n is the number of periods.

In this case:

- C = $8,000 ,

- r = 6 % or 0.06 ,

- n = 20 .

Let's calculate the present value of the annuity:

PV = $8,000 x ( {(1 - (1 + 0.06)^{-20})} / {0.06} )

Using this formula, you can find the present value of the annuity. If the present value is greater than $100,000, Jane should choose the annuity; otherwise, she should choose the lump sum.