SOLUTION: Lorenzo and Michael each decide to invest in a mutual fund to save for retirement. They each choose a mutual fund that has had an average return of 5.6% over the last decade. There

Algebra ->  Equations -> SOLUTION: Lorenzo and Michael each decide to invest in a mutual fund to save for retirement. They each choose a mutual fund that has had an average return of 5.6% over the last decade. There      Log On


   

Question 1131242: Lorenzo and Michael each decide to invest in a mutual fund to save for retirement. They each choose a mutual fund that has had an average return of 5.6% over the last decade. There is no guarantee that the mutual fund will continue to earn this same rate, but it can be used as an estimate of future returns. Use the information given below to estimate how much each man will have when he retires. Round to the nearest dollar. Hint: The amount earned is how much they have without the initial investment.
Lorenzo invests $3,000 when he is 25 years old.
Michael invests $5,000 when he is 45 years old.
Both men plan to retire at age 65.
How much money will Lorenzo have at retirement? How much did he earn?
How much money will Michael have at retirement? How much did he earn?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Lorenzo invests $3000; it accumulates interest at a rate of 5.6% per year (yearly growth factor 1.056) for 40 years (65-25):

3000%281.056%29%5E40+=+26526

Michael invests $5000; it accumulates interest at a rate of 5.6% per year (yearly growth factor 1.056) for 20 years (65-45):

5000%281.056%29%5E20+=+14868

Lorenzo has $26,526 at retirement; he earned $26526-$3000 = $23,526.

Michael has $14,868 at retirement; he earned $14868-$5000 = $9868.

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Added in response to reader's question

The growth factor is the number the current value gets multiplied by each time interest is accumulated. It is equal to 1 plus the interest rate.

5.6% interest rate --> 0.056 as a decimal --> 1+0.056 = 1.056 growth factor