Suppose a deposit of R dollars is made at the end of each year, and assume an APR of r% compounding continuously. (a) If we invest like this for 3 years, what is the value of the account after the third year? (b) If we are making these payments for 3 years, how much money must we invest today to cover the payments? (c) If we make these payments in perpetuity, find a formula which describes the amount of principal we must invest today to cover all future payments. (d) If we invest like this for three years, but instead use an account with an APR s% compounded weekly, determine s so that this second account has the same value as your answer in part (a) after three years.
Suppose a deposit of R dollars is made at the end of each year, and assume an APR of r% compounding continuously. (a) If we invest like this for 3 years, what is the value of the account after the third year? (b) If we are making these payments for 3 years, how much money must we invest today to cover the payments? (c) If we make these payments in perpetuity, find a formula which describes the amount of principal we must invest today to cover all future payments. (d) If we invest like this for three years, but instead use an account with an APR s% compounded weekly, determine s so that this second account has the same value as your answer in part (a) after three years.
Chapter11: Capital Budgeting Decisions
Section: Chapter Questions
Problem 3PB: Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate...
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Suppose a deposit of R dollars is made at the end of each year, and assume an APR of r% compounding continuously.
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(a) If we invest like this for 3 years, what is the value of the account after the third year?
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(b) If we are making these payments for 3 years, how much money must we invest today to cover the payments?
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(c) If we make these payments in perpetuity, find a formula which describes the amount of principal we must invest today to cover all future payments.
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(d) If we invest like this for three years, but instead use an account with an APR s% compounded weekly, determine s so that this second account has the same value as your answer in part (a) after three years.
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VIEWStep 2: a. Value of Account after third year (FV):
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VIEWStep 4: c. Amount need to be invested today if payments are made for perpetuity:
VIEWStep 5: d. Calculation of Rate equal to rate of continous compoudning
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