Question

If Angelica instead plans to purchase a nice home on the coast with her lumpsum lottery winnings right now, but also wants to purchase an island in the Mediterranean when she retires in 20 years, how much would she need to invest each year in order to reach the same total investment value as in part (b) (consider both the 12% and 5% options)? (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answers to 2 decimal places e.g. 5,125.36.) Attempts: 0 of 3 used If Angelica chooses the lump-sum payment, she will invest it and try not to touch any of the earnings until her retirement. She will then use the entire value of the investment to purchase an island in the Mediterranean. If she plans to retire in 20 years and her investment consistently earns 12% annually, how much will her budget be for the island? (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answer to 2 decimal places e.g. 5,125.36.) Budget $ What if the investment earns only 5% annually?

Answer 1

To find out how much Angelica would need to invest annually for 20 years to reach a particular investment value, we would calculate the annual contributions that compound to the same future value at the given interest rates (12% and 5%). We would use the future value of an annuity formula and solve for the annual payment.

Step-by-step explanation:

To determine how much Angelica would need to invest annually to reach the same total investment value as in part (b) at retirement in 20 years, we must estimate the annual contribution that would result in the same future value (FV) when the investments grow at a particular rate of interest. Using the formula for future value of an annuity:

FV = Pmt × [((1 + r)^n - 1) / r]

Where:

• Pmt is the annual payment
• r is the annual interest rate (as a decimal)
• n is the number of years until retirement

Angelica would need to invest each year in such a way that when compounded annually at either 12% or 5%, the future value at retirement matches the intended budget for purchasing the island. To find the exact annual investment, the above formula would be rearranged to solve for Pmt, given the desired FV, n, and r.

Keep in mind that higher rate investments would require a smaller annual payment due to the greater effects of compound interest, while lower rates will necessitate a larger annual investment.