Question

You have borrowed $28,000 at an interest rate of 12% compounded annually. Equal payments will be made over a four-year period, with each payment made at the end of the corresponding year. What is the amount of the annual payment foe the second year?

Answer 1

Answer:

$A = 28000 [\frac{0.12 (1.12)^4}{(1.12)^4 -1}]$

$A = 28000 [\frac{0.12*1.574}{1.574-1}]$

$A=28000*0.3292 = 9218.564$

So then the annual pay would be $ 9218.564 for this case

Explanation:

For this question we can use the Equivalent annual value (A) given by the following expression:

$A = PV [\frac{i (1+i)^t}{(1+i)^t -1}]$

Where $PV = 28000$ represent the pesent value

$i = 0.12$ since the rate is yearly

$t = 4$ since we have 4 years to pay

So then we have everything to replace and we got:

$A = 28000 [\frac{0.12 (1.12)^4}{(1.12)^4 -1}]$

$A = 28000 [\frac{0.12*1.574}{1.574-1}]$

$A=28000*0.3292 = 9218.564$

So then the annual pay would be $ 9218.564 for this case

And this amount would be paid each year in order to pay all the money after 4 years.