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Jamal wants to invest $150 every month for 10 years.   At the end of that time he...

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lbawa | Student, Undergraduate | (Level 1) Honors

Posted January 13, 2013 at 10:19 PM via web

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Jamal wants to invest $150 every month for 10 years.   At the end of that time he would like to have $25000. 

At what annual interest rate, compounded monthly, does Jamal need to invest to reach his goal?

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted January 14, 2013 at 12:18 AM (Answer #1)

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This question is related to the future value of growing annuity. It is given by;

`FV = A((1+i)^n-1)/i`

 

FV = Future value of the time period n

A = Initial payment at n=1

i = compound rate

n = number of payment period considered

 

For the question;

FV = $25000

A = $150

n = 120 months

 

`FV = A((1+i)^n-1)/i`

`25000 = 150((1+i)^120-1)/i`

`(25000/150) = ((1+i)^120-1)/i`

 

For ease of calculation we can set `(1+i) = r`

Then ;

`(25000/150) = (r^120-1)/(r-1)`

No using a scientific calculator you can solve this.

It will give r as;

`r = 1.00525`

`i = 0.00525`

 

So the monthly interest rate `= 0.00525xx100`

Annual interest rate `= 0.00525xx100xx12 = 6.31%`

 

So the annual interest rate would be 6.31%.

 

 

Sources:

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sibun | Student, Grade 12 | (Level 1) Honors

Posted March 7, 2013 at 5:02 PM (Answer #2)

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This question is related to the future value of growing annuity. It is given by;

 

FV = Future value of the time period n

A = Initial payment at n=1

i = compound rate

n = number of payment period considered

 

For the question;

FV = $25000

A = $150

n = 120 months

 

 

For ease of calculation we can set 

Then ;

No using a scientific calculator you can solve this.

It will give r as;

 

So the monthly interest rate 

Annual interest rate 

 

So the annual interest rate would be 6.31%.

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