.. Suppose r, s > 0 are interest rates. You invest in an account which compounds at the end of each month according to the following schedule: Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Rate r r r r (i) If you invest P dollars into this account on January 1st, and this is the only deposit that you make, what is the value of the account after one year? (ii) Suppose you invest P dollars on January 1st of every year. What is the value of the annuity after n-years? Express your answer without using a sum. (iii) Suppose you invest P dollars on January 1st, April 1st, July 1st, and October 1st of each year. What is the value of the annuity after n-years? Express your answer without using a sum.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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1. Suppose r, s > 0 are interest rates. You invest in an account which compounds at the end of each month
according to the following schedule:
Apr
Мay
Aug Sep
Nov
Month
Jan
Feb
Mar
Jun
Jul
Oct
Dec
Rate
S
r
S
r
(i) If you invest P dollars into this account on January 1st, and this is the only deposit that you make,
what is the value of the account after one year?
(ii) Suppose you invest P dollars on January 1st of every year. What is the value of the annuity after
n-years? Express your answer without using a sum.
(iii) Suppose you invest P dollars on January 1st, April 1st, July 1st, and October 1st of each year.
What is the value of the annuity after n-years? Express your answer without using a sum.
Transcribed Image Text:1. Suppose r, s > 0 are interest rates. You invest in an account which compounds at the end of each month according to the following schedule: Apr Мay Aug Sep Nov Month Jan Feb Mar Jun Jul Oct Dec Rate S r S r (i) If you invest P dollars into this account on January 1st, and this is the only deposit that you make, what is the value of the account after one year? (ii) Suppose you invest P dollars on January 1st of every year. What is the value of the annuity after n-years? Express your answer without using a sum. (iii) Suppose you invest P dollars on January 1st, April 1st, July 1st, and October 1st of each year. What is the value of the annuity after n-years? Express your answer without using a sum.
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