# Math Help - Present Value of an ordinary simple annuity

1. ## Present Value of an ordinary simple annuity

A 20 year loan requires semiannual payments of $1073.33 including interest at 6.8% compounded semiannually. a) what was the original amount of the loan? FV = PMT ((( 1 + i)^n - 1)/i) i = 0.068 / 2 1073.33 (1 + 0.034)^40 - 1 ) _______________ 0.034 FV = 85 704.59 85,704.59 = pv ( 1 + 0.034 )^40 Pv = 22,500 B) What is the loan's balance 8.5 years later (just after the scheduled payment) 22 500 ( 1 + 0.034)^17 or 85 704.59/(1+0.034)^40 - 1 ) thats where i'm stuck 2. Originally Posted by diehardmath4 A 20 year loan requires semiannual payments of$1073.33 including interest at 6.8% compounded semiannually.
Check that 1073.33: doesn't "work"; typo?

3. ## YEa it was a typo after i checked

A 20 year loan requires semiannual payments of 1037.33 including interest at 6.8% compounded semiannually.

a) what was the original amount of the loan?

b) What is the loan's balance 8.5 years later ( just before the scheduled payment ) ?

4. Originally Posted by diehardmath4
A 20 year loan requires semiannual payments of 1037.33 including interest at 6.8% compounded semiannually.

a) what was the original amount of the loan?

b) What is the loan's balance 8.5 years later ( just before the scheduled payment ) ?
a) 22500 is correct. Simply get FV of the payments:
1037.33(1 - 1/1.034^40) / .034 = 22500

b) I'm assuming you mean "just after", as in your original post:
x = FV of 22500 for n = 17
y = FV of 1037.33 payment for n = 17
owing 8.5 years later = x - y