+598 A contract valued at $27,500 requires payments of $6000 every six months. The first payment is due in four years and interest is at 11% compounded semi-annually.
(a)How many payments are required?
(b)What is the size of the last payment?
(c) How much will be paid in total?
(d) how much of what is paid is interest?
Any help with steps would be greatly appreciated. Thanks
A contract valued at $27,500 requires payments of $6000 every six months. The first payment is due in four years and interest is at 11% compounded semi-annually.
(a)How many payments are required?
(b)What is the size of the last payment?
(c) How much will be paid in total?
(d) how much of what is paid is interest?
Any help with steps would be greatly appreciated. Thanks
Since the 1st.payment is not due for 4 years, then we have to find the FV of the $27,500 at the given rate of 11% S.A., which comes to=$42,203.88. Now this loan has to be paid in $6,000 S.A. payments.
a-9.14 payments are required.
b-The size of the last payment will be =$6,440.29P + $354.22 Int.=$6,794.51.
c-$6,000 X 8 + $6,794.51=$54,794.51 Total payments.
d-54,794.51 - $42,203.88=$12,590.63 Total interest paid.
The formulae used here are:FV=PV[1 + R]^N=FV OF $27,500 TODAY. and,
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}=PMT NEEDED TO PAY OFF A LOAN OF $42,203.88,
Where R=Interest rate per period, N=number of periods, P=periodic payment. PV=Present value, FV=Future value.
