math problem payment size2

Mathematics
Tutor: None Selected Time limit: 1 Day

Suppose payments will be made for 9 

1
4
 yr at the end of each month into an ordinary annuity earning interest at the rate of 6.25%/year compounded monthly. If the present value of the annuity is $34,000, what should be the size of each payment? 
Dec 9th, 2014

Suppose payments will be made for 9 yr at the end of each month into an ordinary annuity earning interest at the rate of 6.25%/year compounded monthly. If the present value of the annuity is $34,000, what should be the size of each payment? 


I am not sure of the exact problem due to the formatting of your question. I am going to answer the problem assuming you meant 9 years. You should be able to plug in the correct variables if my assumption is wrong.


Use the Present Value of Annuity Formula

PV = A × [(1 - (1/(1 + r)^n))/r]     Solved for A:    A = PV × [r/(1 - (1 + r)^-n)]     


Where,

PV = present  value of annuity

A = annuity payment 

r = interest rate

n = number of time periods


In this case,

PV = $34,000

A = annuity payment 

r = .0625/12 = .0052083 (divide interest rate by 12 since it is compounded monthly)

n = 9 * 12 = 108 (multiply number of years by 12 since compounded monthly)


A = 34000 × [.0052083/(1 - (1 + .0052083)^-108)]        plug in known variables

A = 34000 × [.0052083/(1 - (1.0052083)^-108)]            simplify 

A = 34000 × [.0052083/(1 - .570616)]                           simplify

A = 34000 × [.0052083/.429385]                                  simplify

A = 34000 × .0121298                                                  simplify

A = $412.41           

I hope this helps. Good Luck!


Dec 11th, 2014

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