Question

A $20,000 loan is to be amortized for 10 years with quarterly payments of $699.44. If the interest rate is 7%, compounded quarterly, what is the unpaid balance immediately after the sixth payment

Answer 1

The answer is "17809.46"

Step-by-step explanation:

Given:

P= $20,000

quarterly payment k= $699.44

interest rate quarterly r= 7%

`r=(7)/(400)\\\\r= 0.0175`

n=6

Formula:

`\ unpaid \ balance = P(1+r)^n-K* ((1+r)^n-1)/(r)`

`=20,000(1+0.0175)^6-699.44* ((1+0.0175)^6-1)/(0.0175)\\\\=20,000(1.0175)^6-699.44* ((1.0175)^6-1)/(0.0175)\\\\=20,000* 1.10970235-699.44* (1.10970235-1)/(0.0175)\\\\=22,194.047-699.44 * (0.10970235)/(0.0175)\\\\=22,194.047-699.44 * 6.26870571\\\\=22,194.047-4384.58352\\\\=17809.4635\\\\`

The final answer is "
`\bold{= 17809.46}\\`".