payments problem..?
Posted by MarkMay 24
100,000 has been borrowed from the bank at a discount rate of 24% compounded monthly over 48 months. Repayments are every month.
Use your Financial Tables.
1. How much are the periodic payments?
2. How much is the last payment?
3. How much of that is interest?
4. How much of that is repayment of principle amount outstanding ?
how can I solve this one??????
1) 100000 = x(1-1/(1.02)^48))/.02 = 30.673x, so x = 3260.18
2) Last payment should equal monthly payment
3) 3260. 18 – 3260.18/1.02 = 63.92 in interest.
4) 3260.18/1.02 = 3196.26
The rate of 24% compounded monthly means that the rate per month is 0.24/12 = 0.02.
1) Find the PRESENT VALUE (using your financial table) at a rate of (i=2%) and time of 48 (n=48). You should come up with 30.67312. If you cannot find it, the formula is:
PV(i=2%,n=48) = (1-1.02^-48)/0.02
Then, divide 100,000 by this value:
100000/30.67312 = 3260.18
This will be the monthly payment.
2) The payments are the same (periodic) each month, so that the last payment is still 3260.18.
3) Consider this:
at the 47th (second to the last) payment, the outstanding balance is 3,196.26. There is a formula for this:
use the table to get the present value at 2% and period 1:
formula: (1-1.02^-1)/0.02 = 0.980392
**Note, this uses the PROSPECTIVE method of finding the balance, which is simply the present value of all future payments – one in this case
Multiply this to the payment of 3260.18 to get the outstanding balance of 3196.26.
On the last period (48th), the interest is 2% of the outstanding balance of the 47th: 0.02×3196.26 = 63.93.
4) Since out of the monthly payment of 3260.18 the amount 63.93 was used for interest, the remaining:
3260.18 – 63.93 = 3196.58
will be used for the principal repayment.