2-61. As a bank employee, you've been asked to determine the pricing of an annuity for a client. The client would like to receive lump sum payments of $50,000 at the beginning of each year for the next 10 years. The first payment would be made immediately upon purchasing the annuity, so that there are exactly 10 payments. (a) The bank wants to make a profit off selling this annuity. If the bank calculates it can make an annualized return of r off the initial lump sum payment, should the bank calculate the cost of the annuity at a rate higher or lower than r? (b) If the bank calculates annuities at an APR of 3% compounding at the end of each month, what should you charge the client?
2-61. As a bank employee, you've been asked to determine the pricing of an annuity for a client. The client would like to receive lump sum payments of $50,000 at the beginning of each year for the next 10 years. The first payment would be made immediately upon purchasing the annuity, so that there are exactly 10 payments. (a) The bank wants to make a profit off selling this annuity. If the bank calculates it can make an annualized return of r off the initial lump sum payment, should the bank calculate the cost of the annuity at a rate higher or lower than r? (b) If the bank calculates annuities at an APR of 3% compounding at the end of each month, what should you charge the client?
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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Transcribed Image Text:2-61. As a bank employee, you've been asked to determine the pricing of an annuity for a client.
The client would like to receive lump sum payments of $50, 000 at the beginning of each year
for the next 10 years. The first payment would be made immediately upon purchasing the
annuity, so that there are exactly 10 payments.
(a) The bank wants to make a profit off selling this annuity. If the bank calculates it can
make an annualized return of r off the initial lump sum payment, should the bank
calculate the cost of the annuity at a rate higher or lower than r?
(b) If the bank calculates annuities at an APR of 3% compounding at the end of each month,
what should you charge the client?
(c) To make your life easier in the future, you decide to calculate the charge for this annuity
if the yearly payment is R dollars over N years (N total payments). What is the charge
for such an annuity?
(d) The original client changed their mind, and wishes to purchase a perpetuity instead.
What should you charge them?
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