+0  
 
0
89
1
avatar

A loan for $1,000,000 is granted by the Bank to ABC Importing Company. The loan is to be repaid in 10 years and bears an interest rate of 5% compounded monthly. The annual payments will start with P for the first year and decrease by 2% annually thereafter. What is the initial payment that ABC Company must pay to the Bank? And how much interest will cost the Company over the 10-year period? Thank you for any help.

Guest May 24, 2017
Sort: 

1+0 Answers

 #1
avatar
0

It is little ambiguous about the 2% decrease in payments. For this purpose, I shall assume that the payments will decrease by 2% from the previous payment. In other words the payments will decrease as follows: $1, $0.98, $0.9604(0.98 x 0.98), $0.941192(0.9604 x 0.98), 0.98^4....etc. to the 10th payment.

 

The interest rate is 5% compounded monthly. Will adjust it to compounded annually to match the annual payments, which comes to =5.11618978817%. 

Now, we just find the Present Value of the above payments, which comes to =7.08110996994. And then the annual, or initial payment, will be =$1,000,000 / 7.08110996994 =$141,220.80. This payment will decrease by 2% annually from the previous payment.

 

To calculate the interest paid by the ABC Company, we simply have to add the 10 payments which come to a total of =$1,291,656.23. By subtracting the loan of $1,000,000 we get =$291,656.23 total interest paid by the Company over a period of 10 years.

 

P.S. There is a specific formula used for such problems, which is rarely used, but comes in as very handy in calculating such problems. It is written like this: PV = P*(((1+G) / (1+R))^N - 1) / (G-R), where G =% increase or decrease in payment, R=Interest rate per period, N=Number of periods, P=Periodic payment, PV=Present Value.

Guest May 24, 2017

13 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details