Simple Interest
October 20, 2022
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October 20, 2022Â About this post
In this topic we will learn to solve problems which are concerned with finding the interest on the amount that is originally lent, borrowed or invested as well as on the accumulated interest of previous periods.
The first section in this topic is an introduction to compound interest with an explanation of the terminologies involved, the formula used to compute compound interest. You will learn about annual and non-annual compounding. And then we have shared some important tips on compound interest. The exercises contain solved question and answers on compound interest. When solving exercises, we recommend you to try solving the problems on your own, that way you will understand better and you can define your own approach to solving problems on compound interest.
Introduction to Simple Interest
Compound Interest is the extra amount that is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. This addition of interest to the principal is called compounding. Compound Interest is denoted by CI.
Principal: The amount borrowed (or invested) is called the Principal generally denoted by P.
Amount: Denoted by A is the final value of principal with interest. (Normally it is the future value)
Rate of interest: Is the annual simple interest rate. Denoted by r.
Interest: Denoted by I. Is the extra amount by which the principal increases.
Time period: Is the time interval for which the money is borrowed (or invested). Denoted by n.
Compound Interest problem involves two rates depending on which the amount A is calculated
- Annual rate :
The amount A at the end of ‘t’ time periods at a rate of interest of r% p.a is given by
A = P(1 + $\frac{r}{100})^t$.
- The rate per compounding period, i = $\frac rm$
In this case, the amount A is given by
A = P(1 + $\frac{i}{100)^n}$
where i = $\frac rm$ (i is the interest rate per period)
n = mt (n is the total number of compounding periods)
m - number of compounding periods per year
t - time in years
The compounded interest CI = A - P.
Effective rate of interest
If an amount is compounded yearly once at a certain rate of interest, that interest is called as nominal interest. But if the interest is compounded more than once (Ex. half yearly or quarterly compounding) the rate of interest exceeds the per annum nominal interest rate. This exceeded rate of interest is called as Effective rate of interest.
Important Points:
- Unlike Simple Interest, the Compound Interest earned every year is not constant.
- The principal is same at the beginning of every year.
- Number of years for an amount to double itself at CI r% pa is approx. given by $\frac{72}{r}$% years.
The error in the answer increases if r<5% or r>20%
- When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively.
Amount = P(1+$\frac{R1}{100})(1+\frac{R2}{100})(1+\frac{R3}{100})$
