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find the final amount in this retirement account, in which the rate of return on the account and the regular contribution change over time  1500$ per quarter invested at 7.9% compound quarterly , for 20 years, then 1000$ per quarter invested at 6.8% compund quarterly for 10 years.    answer is about 620,187$

find the final amount in this retirement account, in which the rate of return on the account and the regular contribution change over time  1500$ per quarter invested at 7.9% compound quarterly , for 20 years, then 1000$ per quarter invested at 6.8% compund quarterly for 10 years.    answer is about 620,187$

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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find the final amount in this retirement account, in which the rate of return on the account and the regular contribution change over time 

1500$ per quarter invested at 7.9% compound quarterly , for 20 years, then 1000$ per quarter invested at 6.8% compund quarterly for 10 years. 

 

answer is about 620,187$

# 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) \( A = P \left(1 + \frac{\text{APR}}{n}\right)^{nt} \) 5) **Continuous Compounding** - \( A = P \cdot e^{(\text{APR} \times Y)} \) or \( A = Pe^{rt} \) ## ANNUAL PERCENTAGE YIELD 6) \( \text{APY} = \left(\frac{\text{year end balance - starting balance}}{\text{Starting balance}}\right) \times 100\% \) 7) \( \text{APY} = \left(1 + \frac{\text{APR}}{n}\right)^{n} - 1 \) - Calculator: \( = (1 + \text{APR} − n)^1 - 1 \) ## SAVINGS PLANS 8) \( A = \text{PMT} \times \frac{\left(1 + \frac{\text{APR}}{n}\right)^{nY} - 1}{\frac{\text{APR}}{n}} \) - Calculator: \( = \text{PMT} ((1 + \text{APR} - n)^{Y} - 1) + (\text{APR} + n) \) 9) \( \text{PMT} = A \times \frac{\frac{\text{APR}}{n}}{\left(1 + \frac{\text{APR}}{n}\right)^{nY} - 1} \) - Calculator: \( = A(\text{APR} − n) + ((1 + \text{APR} − n)^{Y} − 1) \) ## LOAN PAYMENT FORMULA 10) \( \text{PMT} = P \times \left(\frac{\frac{\text{APR}}{n}}{1 - \left(1 + \frac{\text{APR}}{n}\right)^{-nY}}\right) \) - Calculator: \(
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) \( A = P \left(1 + \frac{\text{APR}}{n}\right)^{nt} \) 5) **Continuous Compounding** - \( A = P \cdot e^{(\text{APR} \times Y)} \) or \( A = Pe^{rt} \) ## ANNUAL PERCENTAGE YIELD 6) \( \text{APY} = \left(\frac{\text{year end balance - starting balance}}{\text{Starting balance}}\right) \times 100\% \) 7) \( \text{APY} = \left(1 + \frac{\text{APR}}{n}\right)^{n} - 1 \) - Calculator: \( = (1 + \text{APR} − n)^1 - 1 \) ## SAVINGS PLANS 8) \( A = \text{PMT} \times \frac{\left(1 + \frac{\text{APR}}{n}\right)^{nY} - 1}{\frac{\text{APR}}{n}} \) - Calculator: \( = \text{PMT} ((1 + \text{APR} - n)^{Y} - 1) + (\text{APR} + n) \) 9) \( \text{PMT} = A \times \frac{\frac{\text{APR}}{n}}{\left(1 + \frac{\text{APR}}{n}\right)^{nY} - 1} \) - Calculator: \( = A(\text{APR} − n) + ((1 + \text{APR} − n)^{Y} − 1) \) ## LOAN PAYMENT FORMULA 10) \( \text{PMT} = P \times \left(\frac{\frac{\text{APR}}{n}}{1 - \left(1 + \frac{\text{APR}}{n}\right)^{-nY}}\right) \) - Calculator: \(
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