Question

5. You have a bank loan at 6.75%, compounded monthly with quarterly payments. What is the effective interest rate per payment period?

6. You lent $500 to your friend at 10% compounded every 2 months. You have asked her to pay the money back at the end of one year and to make an interest payment every six months (one at the 6 month mark and one at the end). What is the effective interest rate per payment period?

7. You borrow $1,300 at 7% annual interest rate, compounded monthly. You will make annual payments to pay off the balance and interest. What is the effective interest rate per payment period?

8. You borrow $15,000 to purchase a car. The credit union requires you to make quarterly payments, but compounds interest monthly. Your loan is at 8% for 3 years. What is your quarterly payment amount?

9. You are an independent contractor who gets paid at the conclusion of each contract. Because these contracts conclude at different intervals, it is difficult to have a consistent amount of cash on hand at the end of each month. When you negotiated your mortgage you worked out a deal that you would make annual payments, but that the interest would be compounded monthly. The annual interest rate is 5.25% and you have annual payments of $15,000 for 15 years. How much did you borrow?

Answer 1

Answer to Finance Question No5

Calculation of effective rate per payment period

Rate=6.75% compounded monthly

Payment Frequency= Quarterly

We know that monthly compounding means that every month, interest shall be charged on my loan amount as well as unpaid interest. As per question, payments are quarterly and we need to calculate the quarterly effective rate. The formula to convert the compounding rate to effective rate is as below

r = (1+i/n)^n-1 where

r= Effective rate on payment

i= monthly compounding rate or given rate=6.5%

n= number of compounding months per payment=3 since quarterly payment

Now putting the values in formula

r= (1+6.5%/3)^3-1

r=6.64%

Hence the answer is that effective payment rate per payment period i.e. quarterly is 6.64%

Answer to Finance Question No6

            Calculation of effective rate per payment period

We know that bimonthly compounding means that every 2 months, interest shall be charged on my loan amount as well as unpaid interest. As per question, payments are half yearly i.e. every sixth month and we need to calculate the halfyearly effective rate. The formula to convert the monthly compounding rate to effective rate is as below

r = (1+i/n)^n-1 where

r= Effective rate on payment

i= monthly compounding rate or given rate=10.00%

n= number of compounding months per payment=3 since compounding 2months for 6 months period

Now putting the values in formula

r= (1+10%/3)^3-1

r=10.3370% or 10.34%

Hence the answer is that effective payment rate per payment period i.e. half yearly is 10.34%

Answer to Finance Question No7

            Calculation of effective rate per payment period

We know that monthly compounding means that every month, interest shall be charged on my loan amount as well as unpaid interest. As per question, payments are yearly i.e. Annual and we need to calculate the yearly effective rate. The formula to convert the compounding rate to effective rate is as below

r = (1+i/n)^n-1 where

r= Effective rate on payment

i= monthly compounding rate or given rate=7.00%

n= number of compounding months per payment=12 since compounding every month for 12 months period

Now putting the values in formula

r= (1+7%/12)^12-1

r=7.2290% or 7.23%

Hence the answer is that effective payment rate per payment period i.e. yearly is 7.23%

Answer to Finance Question No8

            Calculation of quarterly payment amount.

We know that monthly compounding means that every month, interest shall be charged on my loan amount as well as unpaid interest. As per question, payments are quarterly and we need to calculate the quarterly effective rate. The formula to convert the compounding rate to effective rate is as below

r = (1+i/n)^n-1 where

r= Effective rate on payment

i= monthly compounding rate or given rate=8.00%

n= number of compounding months per payment=3 since compounding every month for a quarter

Now putting the values in formula

r= (1+8%/3)^3-1

r=8.2152%

Hence the answer is that effective payment rate per payment period i.e. quarterly is 8.2152%. Then the interest amount will $15000*8.2152%=$1232.28

Loan to be divided in 12 quarter ( 3 years *4 quarter per year)=$15000/12=$1250/quarter.

Answer is Total repayment every quarter is $1250+$1232.28=$2482.28

Answer to Finance Question No9

Calculation to find out the borrowed amount

We have following details

1. Payment is annual
2. Interest rate is 5.25% annual
3. Instalment Amount is $15000
4. Period is 15 Years

EMI calculation formula is as shown below

EMI=(P*R*(1+R)^N)/(1+R)^N-1

Where P is principal or loan amount, R is monthly rate (5.25%=5.04%=0.0504

And N is period of Loan i.e. 15 years

Now putting down the values

$15000=(P*0.0504*(1+0.0504)^15)/(1+0.0504)^15-1

$15000=(P*0.0504*(1.0504)^15)/(1.0504)^15-1

$15000=(P*0.0504*2.0908)/1.0908

P*0.105376=$15000*1.0908

P*0.105376=$16362.59

P==$16362.59/o.105376=%155277.70

Answer is that loan amount is $155277.70

Reference

Duflo, J., & Zuker, A. P. (1995). Microscopic mass formulas. Physical Review C, 52(1), R23.

Payette, R. (2008). U.S. Patent Application No. 11/651,395.