Sophia invests $100 at the end of each year for 9 years at an annual effective interest rate of 4%. The interest credited at the end of each year is reinvested at an annual effective rate of 5%. The accumulated value at the end of 12 years is $X. Laura invests $100 at the end of each year for 12 years at an annual effective interest rate of 2.5%. The interest credited at the end of each year is reinvested at an annual effective rate of 3.5%. The accumulated value at the end of 12 years is $Y. Calculate Y X
Sophia invests $100 at the end of each year for 9 years at an annual effective interest rate of 4%. The interest credited at the end of each year is reinvested at an annual effective rate of 5%. The accumulated value at the end of 12 years is $X. Laura invests $100 at the end of each year for 12 years at an annual effective interest rate of 2.5%. The interest credited at the end of each year is reinvested at an annual effective rate of 3.5%. The accumulated value at the end of 12 years is $Y. Calculate Y X
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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Transcribed Image Text:**Problem 2**
Sophia invests $100 at the end of each year for 9 years at an annual effective interest rate of 4%. The interest credited at the end of each year is reinvested at an annual effective rate of 5%. The accumulated value at the end of 12 years is $X.
Laura invests $100 at the end of each year for 12 years at an annual effective interest rate of 2.5%. The interest credited at the end of each year is reinvested at an annual effective rate of 3.5%. The accumulated value at the end of 12 years is $Y.
Calculate \( \frac{Y}{X} \).
**Solution:**
Expert Solution
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SOLUTION:-
| Sophia | |||||||
| Year | Investment | New Value | Interest @ 4% | Accumulated | Reinvestment | Interest @ 5% | Accumulated Amount |
| 1 | $100.00 | $100.00 | $4.00 | $104.00 | $104.00 | ||
| 2 | $100.00 | $204.00 | $8.16 | $212.16 | $4.00 | $0.20 | $216.36 |
| 3 | $100.00 | $316.36 | $12.65 | $329.01 | $8.16 | $0.41 | $337.58 |
| 4 | $100.00 | $437.58 | $17.50 | $455.09 | $12.65 | $0.63 | $468.37 |
| 5 | $100.00 | $568.37 | $22.73 | $591.11 | $17.50 | $0.88 | $609.49 |
| 6 | $100.00 | $709.49 | $28.38 | $737.87 | $22.73 | $1.14 | $761.74 |
| 7 | $100.00 | $861.74 | $34.47 | $896.21 | $28.38 | $1.42 | $926.01 |
| 8 | $100.00 | $1,026.01 | $41.04 | $1,067.05 | $34.47 | $1.72 | $1,103.24 |
| 9 | $100.00 | $1,203.24 | $48.13 | $1,251.37 | $41.04 | $2.05 | $1,294.46 |
| 10 | $1,294.46 | $51.78 | $1,346.24 | $48.13 | $2.41 | $1,396.77 | |
| 11 | $1,396.77 | $55.87 | $1,452.65 | $51.78 | $2.59 | $1,507.01 | |
| 12 | $1,507.01 | $60.28 | $1,567.29 | $55.87 | $2.79 | $1,625.96 | |
| Total Accumulated Amount for Sophia is | $1,626.00 |
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