Final answer:
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.