+0  
 
0
128
1
avatar

A company took a $1,000,000 loan from its local Bank at a rate of 5% compounded semi-annually but payable monthly over a term of 10 years. How many months will it take the company to pay off 50% of the loan? Thank you for help.

Guest Mar 28, 2017
Sort: 

1+0 Answers

 #1
avatar
0

First, we have to convert 5% compounded semi-annually to compounded monthly. We can do that as follows: [1 + 0.05/2]^1/6  - 1 x 1,200 =4.94869855817...%.
Next, we can use this loan formula:
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}, Where R=Interest rate per period, N=number of periods, P=periodic payment, PV=Present value.

Now, will just substitute in the above formula as follows:

PMT =1,000,000 x 0.0494869855817/12 x [1 + 0.0494869855817/12]^(10*12) / [1 + 0.0494869855817/12]^(10*12) - 1]

PMT =4,123.91546514 x 2.56588515.......
PMT =$10,581.49 - This is the monthly payment of the loan.

Next, will use the following formula to solve for N.
-P*[(1-(1+R)^-N)/(R)]+FV*(1+(R))^-N-PV=0
If we plug in P=10,581.49, R=The above monthly interest rate, FV=500,000, and PV =1,000,000, then we solve for N:

N =67.33 months. In other words, on the 67th payment, half the loan, or about $500,000 will have been paid off.

Guest Mar 28, 2017

15 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