Question

Consider a student loan of $25,000 at a fixed APR of 6% for 20 years.a. Calculate the monthly payment.b. Determine the total amount paid over the term of the loan.c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest..a. The monthly payment is $0(Do not round until the final answer. Then round to the nearest cent as needed.)

Answer 1

Given:

P= $25000

r=6%

t=20

a.

Consider the formula to find the monthly payment.

`M=(P.r(1+r)^n)/(\lbrack(1+r)^n-1\rbrack)`
`r=6\text{ \%=}(6)/(100*12)=0.005`
`n=20*12=240`

Substitute P=25000, r=0.005 and n=240, we get

`M=(25000*0.005(1+0.005)^(240))/(\lbrack(1+0.005)^(240)-1\rbrack)`

`M=(413.775559476)/(2.31020447581)`
`M=179.107764619`

Hence the monthly payment is $179.11.

b.

we know that the monthly payment is $179.107764619.

Multiply monthly payment by 240, we get

`179.107764619*240=42985.8635086`

The total amount paid over the term of the loan is $ 42985.86.

c).

Interest = The toal amount -loan.

`\text{Interest}=42985.86-25000=17985.86`

Interest is $ 17985.86.

The percentage paid towards principal is

`=(25000)/(42985.86)*100`

`=58.158659615`

The percentage paid towards principal is 58.2%.

The percentage paid towards interest is

`=(17985.86)/(42985.86)*100`

`=41.841340385`

The percentage paid towards interest is 41.8 %