task
2. To illustrate the use of the effective interest rate formula or the APR, assume you agree to pay $440 for a washing machine. A down payment of $40 is made leaving $400 to be borrowed at a stated interest rate of 10 percent. The loan is to be paid off in 18 equal monthly installments.
The finance charge can be calculated using the simple interest rate formula, I = PRT:
I = $400 x 0.10 x 1.5 = $60
You are borrowing $400 (P) for 1.5 years (T) and you will owe a $60 finance charge (I). But is that the effective interest rate? To find out, use above effective interest rate formula, and assume the number of yearly payments is 12, and the total number of payments is 18. The calculation would look like this:
APR = 2 x 60 x 12 / 460 x (18+1) = 1440 / 8740 = 16.5%
The amount to be repaid includes your $400 loan plus the $60 finance charge or $460.
Let’s further assume that the lender requires a loan application fee of $10 and a processing fee (credit check) of $25 in this situation. The annual percentage rate now needs to reflect the increase in the total finance charge from $60 to $95. So the calculation would be:
APR = 2 x 95 x 12 / 495 x (18+1) = 2280 / 9405 = 24%
In this example, the lender stated a simple interest rate of 10 percent. Yet you actually are paying an effective APR of 24 percent once you add in the fees and you do not have the use of the full loan for the entire loan period.
3. Compound interest arises when interest is added to the principal so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding.
The following formula gives you the total amount one will get if compounding is done:-
Where,
A = Final Amount that will be received
P = Principal Amount (i.e. initial investment) r = Annual nominal interest rate (as a decimal i.e. if interest is paid at 5.5% pa, then it will be 0.055) (it should not be in percentage) n = number
The finance charge can be calculated using the simple interest rate formula, I = PRT:
I = $400 x 0.10 x 1.5 = $60
You are borrowing $400 (P) for 1.5 years (T) and you will owe a $60 finance charge (I). But is that the effective interest rate? To find out, use above effective interest rate formula, and assume the number of yearly payments is 12, and the total number of payments is 18. The calculation would look like this:
APR = 2 x 60 x 12 / 460 x (18+1) = 1440 / 8740 = 16.5%
The amount to be repaid includes your $400 loan plus the $60 finance charge or $460.
Let’s further assume that the lender requires a loan application fee of $10 and a processing fee (credit check) of $25 in this situation. The annual percentage rate now needs to reflect the increase in the total finance charge from $60 to $95. So the calculation would be:
APR = 2 x 95 x 12 / 495 x (18+1) = 2280 / 9405 = 24%
In this example, the lender stated a simple interest rate of 10 percent. Yet you actually are paying an effective APR of 24 percent once you add in the fees and you do not have the use of the full loan for the entire loan period.
3. Compound interest arises when interest is added to the principal so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding.
The following formula gives you the total amount one will get if compounding is done:-
Where,
A = Final Amount that will be received
P = Principal Amount (i.e. initial investment) r = Annual nominal interest rate (as a decimal i.e. if interest is paid at 5.5% pa, then it will be 0.055) (it should not be in percentage) n = number