math problem payment size2
Mathematics

Tutor: None Selected  Time limit: 1 Day 
Suppose payments will be made for 9
1 
4 
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!
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