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You are an investor who purchased $1,000,000 worth of 5 Ceritificates of Deposit (CD's), from your local Bank as follows:
$A in CD's @ 1% for 1 Year.
$B in CD's @ 2% for 2 years.
$C in CD's @ 3% for 3 years.
$D in CD's @ 4% for 4 years.
$E in CD's @ 5% for 5 years.

You wish to receive 5 equal annuity payments. What are the amounts you must purchase in A,B, C,D and E, and what is amount of the 5 equal payments that you will receive in 5 years? Thank you for any help.

 Apr 8, 2020
 #1
avatar+930 
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For this question, it basically asks how much money you put into each CD to get the same amount of money back through different interest rates.

The rates respectively are (1.01), (1.02)...(1.05) and for 5 years, it would be $X * (1.01)^5, $X * (1.02)^5, ... , $X * (1.05)^5. 

 

You can set up the equation A(1.01)^5= B(1.02)^5= C(1.03)^5= D(1.04)^5= E(1.05)^5 and A+B+C+D+E= $1,000,000.

 

 

See if you can work something out with this.

 

Hope it helps!

 Apr 8, 2020
 #2
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+1

a=sumfor(n, 1, 5, (n/100+1)^-n;b=1E6/a;print"$",b;print;n=1;s=0;cycle:c= b/(n/100+1)^n;s=s+c;print"$",c;n++;if(n<=5, goto cycle, 0);print;print"$", s


OUTPUT:
$ 221988.40 - Annuity amount for 5 equal payments.

 

$ 219790.50 - Amount invested in A @ 1% for 1 year.
$ 213368.32 - Amount invested in B @ 2% for 2 years.
$ 203150.84 - Amount invested in C @ 3% for 3 years.
$ 189756.62 - Amount invested in D @ 4% for 4 years.
$ 173933.72 - Amount invested in E @ 5% for 5 years.

$ 1000000.00 - Total amounts invested.

 Apr 8, 2020
 #3
avatar+930 
0

Looks good! laugh

 Apr 8, 2020

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