find the interest rate with annual compunding that makes the statement true. 782$ grows to 1071.53$ in 10 years answer is 3.2%
find the interest rate with annual compunding that makes the statement true. 782$ grows to 1071.53$ in 10 years answer is 3.2%
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
find the interest rate with annual compunding that makes the statement true.
782$ grows to 1071.53$ in 10 years
answer is 3.2%
![**Formulas – CH. 4-1332**
**Simple Interest**
1) \( I = Prt \)
2) \( A = P + Prt \)
3) \( A = P(1 + rt) \)
**Compound Interest**
- Formula for interest paid \( n \) times per year:
4) \( A = P \left( 1 + \frac{\text{APR}}{n} \right)^{nY} \)
5) Continuous compounding:
\( A = P \cdot e^{(\text{APR} \cdot Y)} \) or \( A = Pe^{rt} \)
**Annual Percentage Yield**
6) \( \Delta PY = \left( \frac{\text{year end balance} - \text{starting balance}}{\text{starting balance}} \right) \times 100\% \)
7) \( \Delta PY = \left( 1 + \frac{\text{APR}}{n} \right)^{n} - 1 \)
*(= (1 + APR \div n)ⁿ - 1) - Calculator*
**Savings Plans**
8) \( A = \text{PMT} \times \left[ \frac{\left( 1 + \frac{\text{APR}}{n} \right)^{nY} - 1}{\frac{\text{APR}}{n}} \right] \)
- PMT \(\left((1 + \text{APR} \div n)^{nY} - 1)\div(\text{APR} \div n)\right)\)
9) \( PMT = A \times \left[ \frac{\frac{\text{APR}}{n}}{\left( 1 + \frac{\text{APR}}{n} \right)^{nY} - 1} \right] \)
- A(\text{APR} \div n)\div\((1 + (\text{APR} \div n)^{nY} - 1)\)
**Loan Payment Formula**
10) \( PMT = P \times \left[ \frac{\frac{\text{APR}}{n}}{1 - \left( 1 + \frac{\text{APR}}{n} \right)^{-nY}} \right] \)
- P(\text{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc702ff9-d3e6-4e4b-abbc-7bc2699ae04d%2F702fff38-9dd5-4c08-ba5a-eca2c4b50a1a%2Fx777xz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Formulas – CH. 4-1332**
**Simple Interest**
1) \( I = Prt \)
2) \( A = P + Prt \)
3) \( A = P(1 + rt) \)
**Compound Interest**
- Formula for interest paid \( n \) times per year:
4) \( A = P \left( 1 + \frac{\text{APR}}{n} \right)^{nY} \)
5) Continuous compounding:
\( A = P \cdot e^{(\text{APR} \cdot Y)} \) or \( A = Pe^{rt} \)
**Annual Percentage Yield**
6) \( \Delta PY = \left( \frac{\text{year end balance} - \text{starting balance}}{\text{starting balance}} \right) \times 100\% \)
7) \( \Delta PY = \left( 1 + \frac{\text{APR}}{n} \right)^{n} - 1 \)
*(= (1 + APR \div n)ⁿ - 1) - Calculator*
**Savings Plans**
8) \( A = \text{PMT} \times \left[ \frac{\left( 1 + \frac{\text{APR}}{n} \right)^{nY} - 1}{\frac{\text{APR}}{n}} \right] \)
- PMT \(\left((1 + \text{APR} \div n)^{nY} - 1)\div(\text{APR} \div n)\right)\)
9) \( PMT = A \times \left[ \frac{\frac{\text{APR}}{n}}{\left( 1 + \frac{\text{APR}}{n} \right)^{nY} - 1} \right] \)
- A(\text{APR} \div n)\div\((1 + (\text{APR} \div n)^{nY} - 1)\)
**Loan Payment Formula**
10) \( PMT = P \times \left[ \frac{\frac{\text{APR}}{n}}{1 - \left( 1 + \frac{\text{APR}}{n} \right)^{-nY}} \right] \)
- P(\text{
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