Question

Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly. What will his balance be after he has made exactly half of his monthly payments

Answer 1

Answer: 21,990.07

Step-by-step explanation: A P E X

Answer 2

Answer:

The balance be after he has made exactly half of his monthly payments is $56881.4.

Step-by-step explanation:

Given : Dean took out a 10-year loan for $40,000 at an APR of 4% compounded monthly.

To find : What will his balance be after he has made exactly half of his monthly payments?

Solution :

Formula of monthly payment ,

$M=\frac{\text{Amount}}{\text{Discount factor}}$  

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$  

Where, Amount = $40,000

Rate r= 4% compounded monthly

$i=\frac{4}{100}=0.04$  

Time = 10 years  

$n=10\times12=120$  

Now, put all the values we get,  

$D=\frac{1-(1+i)^{-n}}{i}$  

$D=\frac{1-(1+0.04)^{-120}}{0.04}$  

$D=\frac{1-(1.04)^{-120}}{0.04}$  

$D=\frac{1-0.00903}{0.04}$  

$D=\frac{0.9909}{0.04}$  

$D=24.7725$  

$M=\frac{\text{Amount}}{\text{Discount factor}}$  

$M=\frac{40000}{24.7725}$  

$M=1614.69$  

Half of the monthly payment is $807.345

Payment for 10 years is $807.345\times 120=96881.4$

The balance is $96881.4-$40000=$56881.4

Therefore, The balance be after he has made exactly half of his monthly payments is $56881.4.