Question

In: Accounting

A loan of $9,000 is to be repaid in 3 equal payments 60, 180, and 300...

A loan of $9,000 is to be repaid in 3 equal payments 60, 180, and 300 days respectively after the date of the loan.

If the interest rate charged on the loan is 7¼%, what will be the size of each equal payment?  (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Solutions

Expert Solution

Let X be the Amount of Installment

Present value of 3 Installments at 7.25% p.a. shall equal to Principal Amount i.e. $9000
=> (X/(1+7.25%*60/365))+(X/((1+7.25%*60/365)*(1+7.25%*120/365)))+(X/((1+7.25%*60/365)*(1+7.25%*120/365)*(1+7.25%*120/365))) = $ 9,000.00
=> X[(1/(1+7.25%*60/365))+(1/((1+7.25%*60/365)*(1+7.25%*120/365)))+(1/((1+7.25%*60/365)*(1+7.25%*120/365)*(1+7.25%*120/365)))] = $ 9,000.00
=> X[(0.988060930424043)+(0.988060930424043*0.976719293550977)+(0.988060930424043*0.976719293550977*0.976719293550977)] = $ 9,000.00
=> X*2.89571004226829 = $ 9,000.00
=> X = $ 3,108.05

Verification:

On Day Particulars Amount
0 Principal $   9,000.00
Add: Interest for 60 days $       107.26
Less: First Installment $ (3,108.05)
60 Loan Balance $   5,999.21
Add: Interest for next 120 days $       142.99
Less: Second Installment $ (3,108.05)
180 Loan Balance $   3,034.16
Add: Interest for next 120 days $         72.32
Less: Third Installment $ (3,108.05)
300 Loan Balance (Rounding off Difference) $         (1.56)

Note: Assuming that rate of Interest is per annum basis and Annual year consists of 365 days

ekkarill92 answered 3 years ago
Next > < Previous

Related Solutions

Suppose that a loan is being repaid with 60 equal monthly payments, the first coming a...
Suppose that a loan is being repaid with 60 equal monthly payments, the first coming a month after the loan is made. If the rate of interest is 9.7 percent convertible monthly, and the amount of principal in the 22nd payment is 260, how much interest is in the 44th payment?
a) A loan of $5,000 is to be repaid in equal monthly payments over the next...
a) A loan of $5,000 is to be repaid in equal monthly payments over the next 2 years. Determine the payment amount if interest is charged at a nominal annual rate of 15% compounded semiannually. b) Net receipts from a continuously producing oil well add up to $120,000 over 1 year. What is the present amount of the well if it maintains steady output until it runs dry in 8 years if r = 10% compounded continuously?
A firm borrows $5000 and the loan is to be repaid in 4 equal payments at...
A firm borrows $5000 and the loan is to be repaid in 4 equal payments at the end of each of the next 4 years so that the ending balance at the end of year 4 is 0. The interest rate on the loan is 10 percent. The principal repayment in year 3 is:
A firm borrows $5000 and the loan is to be repaid in 4 equal payments at...
A firm borrows $5000 and the loan is to be repaid in 4 equal payments at the end of each of the next 4 years so that the ending balance at the end of year 4 is 0. The interest rate on the loan is 10 percent. The beginning balance in year 2 is:
A $10,000 loan is to be repaid in monthly equal payments in 10 years with an...
A $10,000 loan is to be repaid in monthly equal payments in 10 years with an annual effective interest rate of 19.56% charged against the unpaid balance. What principal remains to be paid after the third payment?
1. A loan is usually repaid in _( Equal OR Unequal )____ payments over a set...
1. A loan is usually repaid in _( Equal OR Unequal )____ payments over a set period of time. 2. Credit cards allow ( One-time OR Repeated )___  use of credit as long as regular _( Monthly OR Annual )_______ payments are made. 3. Your personal financial success depends on your ability to make the sacrifices necessary to ___( Earn OR Spend )___   less than you _( Earn OR Spend )___________ .This means that you should use credit wisely, use credit only...
a loan of 17000 is to be repaid by 4 equal payments due in 2,5,6and 9...
a loan of 17000 is to be repaid by 4 equal payments due in 2,5,6and 9 years respectively. determine the size of the equal payments if the loan was granted at 12% p.a. compounded semi- annually.
A loan L is repaid with annual payments of $500, $400,$300, and $200 at the end...
A loan L is repaid with annual payments of $500, $400,$300, and $200 at the end of each year using a sinking fund method. If the loan has 10%effective interest rate per year and the sinking fund has 8% effective interest our year, find L
Dan borrowed $19,180. The loan is to be repaid by three equal payments due in 89,...
Dan borrowed $19,180. The loan is to be repaid by three equal payments due in 89, 120, and 291 days from now respectively. Determine the size of the equal payments at an interest rate of 10% with a focal date of today. The size of the equal payments is $___ ​(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)
A $37,000 loan at 8.2% compounded semi-annually is to be repaid by equal semi-annual payments over...
A $37,000 loan at 8.2% compounded semi-annually is to be repaid by equal semi-annual payments over 10 years. a) What will be the principal component of the sixth payment? b) What will be the interest component of the sixteenth payment? c) How much will Payments 6 to 15 inclusive reduce the principal? d) How much interest will be paid in the third year? e) What will be the final payment?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT