Kavita borrowed 280,000 from the bank at the rate of 10% per annum. Find the amount payable by her
years if the interest is being compounded half-yearly
Answers
Answer:
The two equal yearly instalments he would have to pay is 12,100. Since the question is “at the end of each year”. monthly, quarterly, semiannual instalments will be different.
simple proof : principal in the beginning (PV) : 21,000
Loan outstanding at the END of year 1 : 21,000+2,100 (10%) = 23,100
Repayment at the END of year 1 : 12,100
Loan outstanding after repayment of 1st yearly instalment : 11,000
Loan outstanding at the END of year 2 : 11,000 + 1100 (10%) = 12,100
FINAL repayment (2nd year) : 12,100
LOAN SETTLED.
you can use the ms excel formula for TVM (time value of money). The parameters to give to the function are PV,PMT,FV,RATE,NPER and TYPE(optional).
a. Use the initial loan amount (21,000 in our case) as PV (present value)
b. our PMT (periodic repayments or equated instalments) is what we need.
c. FV is future value or target loan amount, in our case its full repayment or zero loan balance, its 0. This is useful if you want to compute your instalments to get your loan reduced to a certain target amount say 5,000 instead of full repayment.
d. RATE is the interest rate 10% (yearly) in our case. remember interest rate should correspond to the periods of repayment. in our case its 1 year so we have taken the annual rate of interest, but if you are repaying monthly its 10%/12, quarterly its 10%/4, semiannually its 10%/2 and so on.
e. NPER is the number of periods of repayment. in our case its 2 (years), if its monthly and the target duration for repayment is 2 years then its 24, quarterly its 8, semiannually its 4 and so on.
f. finally TYPE is optional, and takes either 1 or 0, 1 means that you pay in the beginning of the period that is you pay your instalments in advance. 0 means you pay at the end of the Period, i.e you pay at the end of the year. thats our case. so use 0 here.
so the formula is =PMT(10%,2,21000,0,0) which is PMT(rate,nper,pv,fv,type)
the answer will be -12,100 (minus) that signifies that this 12,100 is a cash outflow to the borrower, because you used 21,000 in PV as a positive sum meaning cash inflow to the borrower. conversely if you used -21,000 as a liability of the borrower then you get PMT as positive 12,100 as repayments are assets of the borrower, reducing her liability.