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Welcome to our Math lesson on Calculating the Total Amount Earned when Simple Interest Is Known, this is the third lesson of our suite of math lessons covering the topic of Applications of Percentage in Banking. Simple and Compound Interest, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
From the concept of simple interest, it is clear that the formula which gives the total amount of money (A) a customer receives when he/she deposits a principal P to a bank during a period T if the value of simple interest SI is known, is
When expressing the simple interest in terms of P, T and R, as we did in the previous paragraph, we obtain
Thus,
For example, if a customer deposits $8,700 to a bank (P = 8,700) that offers 2.6% yearly (annual) interest rates (R = 2.6), after a period of 3.5 years of deposit (T = 3.5) he will receive in total:
Obviously, the value of simple interest earned by the customer during this period is the difference between the total amount received and the principal deposited, i.e.
a value that represents 9.1% of the principal ( $791.7/$8700 = 0.091 = 9.1%).
A customer needs to borrow $15,000 from a bank which offers loans with a simple interest rate of 3.8% per annum. The customer hopes to sell property in the future to settle the loan. The property is estimated to cost $18,500. How long after the loan agreement will the customer have to sell the property in order to settle the loan on time?
Clues:
P = 15,000
R = 3.8
A = 18,500
T = ?
Using the combined formula found earlier
we obtain for the time T (in years) needed to settle the loan:
Sometimes, the interest rates are not given per year (annually [per annum]) but per month (monthly [per month]), per 3 months (quarterly), per 6 months (semi-annually), etc. In these situations it is better to have the interest rate expressed per year first, and then apply the formulae we explained above.
A bank offers 0.22% monthly interest rates for loans. How much will a customer receive after three years if he deposits $20,000 now?
We have the following clues:
R (monthly) = 0.22
P = 20,000
T = 3
A = ?
First, we have to calculate the yearly interest rates by multiplying the monthly ones by 12 (the number of months in a year). Thus,
This means the yearly interest is 2.64%.
In this way, we obtain for the money the customer will receive in three years:
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