Question

Suppose you have the following three student​ loans: ​$10000 with an APR of 7.5​% for 12 ​years, ​$15000 with an APR of 8​% for 17 ​years, and ​$13500 with an APR of 9​% for 7 years.

a. Calculate the monthly payment for each loan individually.

b. Calculate the total​ you'll pay in payments during the life of all three loans.

c. A bank offers to consolidate your three loans into a single loan with an APR of 8​% and a loan term of 17 years. What will your monthly payments be in that​ case? What will your total payments be over the 17 ​years?

Answer 1

A)
First loan
=10000*(7.5%/12)/(1-1/(1+7.5%/12)^(12*12))=105.522630861831

Second loan
=15000*(8%/12)/(1-1/(1+8%/12)^(12*17))=134.738526507391

Third loan
=13500*(9%/12)/(1-1/(1+9%/12)^(12*7))=217.202556510519

B)
First loan=10000*(7.5%/12)/(1-1/(1+7.5%/12)^(12*12))*12*12=15195.2588441036

Second loan
=15000*(8%/12)/(1-1/(1+8%/12)^(12*17))*12*17=27486.6594075077

Third loan
=13500*(9%/12)/(1-1/(1+9%/12)^(12*7))*12*7=18245.0147468836

Total=15195.2588441036+27486.6594075077+18245.0147468836=60926.93299849

C)
Monthly payment=(10000+15000+13500)*(8%/12)/(1-1/(1+8%/12)^(12*17))=345.828884702303

Total payment=(10000+15000+13500)*(8%/12)/(1-1/(1+8%/12)^(12*17))*12*17=70549.0924792697