SOLUTION: Jill and Bill are the same age. Jill inherits $20,000 when she is 25, and invests it in an account earning 5% annual interest rate, compounded annually. Bill receives a $20,000 bo

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Jill and Bill are the same age. Jill inherits $20,000 when she is 25, and invests it in an account earning 5% annual interest rate, compounded annually. Bill receives a $20,000 bo      Log On

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Question 1077417: Jill and Bill are the same age. Jill inherits $20,000 when she is 25, and invests it in an account earning 5% annual interest rate, compounded annually. Bill receives a $20,000 bonus at age 35, and then invests it in an account which also earns a 5% annual interest rate, compounded annually. How much more money does Jill have than Bill at age 50?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for annual compound interest, including principal sum, is:
A = P (1 + r/n) (nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
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From age 25 to age 50, Jill's futute value is:
+A%5B1%5D+=+20000%2A%28+1+%2B+.05+%29%5E25+
From age 35 to age 50, Bill's future value is:
+A%5B2%5D+=+20000%2A%28+1+%2B+.05+%29%5E15+
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+A%5B1%5D+-+A%5B2%5D+=+20000%2A%28+1+%2B+.05+%29%5E25+-+20000%2A%28+1+%2B+.05+%29%5E15+
+A%5B1%5D+-+A%5B2%5D+=+20000%2A%28+1.05%5E25+-+1.05%5E15+%29+
+A%5B1%5D+-+A%5B2%5D+=+20000%2A%28+3.386355+-+2.078928+%29+
+A%5B1%5D+-+A%5B2%5D+=+20000%2A1.307427+
+A%5B1%5D+=+A%5B2%5D+=+26148.54+
Jill has $26,148.54 more than Bill at age 50
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Check my math & get another opinion if you like