Quickest Way to Solve Compound Interest Problems

• Compound interest is interest on interest.
• It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously-accumulated interest.
• Compound interest is standard in finance and economics.

Compound Interest Formula

\(A=P\left(1+\frac rn\right)^{nt}\)

P = principal amount (the initial amount you borrow or deposit)
r  = annual rate of interest (as a decimal)
t  = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n  =  number of times the interest is compounded per year

Examples:

Suppose you give Rs100 to a bank which pays you 10% compound interest at the end of every year. After one year you will have Rs100 + 10% = Rs110, and after two years you will have Rs110 + 10% = Rs121.

Problems:

1.An amount of Rs1,500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. What is the balance after 6 years?

Explanation:

Using the compound interest formula, we have that
P = 1500, r = 4.3/100 = 0.043, n = 4, t = 6. Therefore,

\(A=15\left(1+\frac{0.043}4\right)^{4(6)}\approx1,938.84\)

So, the balance after 6 years is approximately Rs1,938.84.

2.The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:

Explanation:

Let the sum be Rs. x. Then,

\(\begin{array}{l}C.I=\left[x\left(1+\frac4{100}\right)^2-x\right]=\left(\frac{676}{625}x-x\right)=\frac{51}{625}x\\S.I=\left(\frac{x\times4x2}{100}\right)=\frac{2x}{25}\\.’.\;\frac{51x}{625}-\frac{2x}{25}=1\\x=625\end{array}\)

3.Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?

Explanation:

\( \begin{array}{l}Amount=Rs\left[8000\times\left(1+\frac5{100}\right)^2\right]\\=Rs\left(8000\times\frac{21}{20}\times\frac{21}{20}\right)\\=8820\end{array}\)

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 Topics covered in this e-book are :

1. Simple Interest
2. Compound Interest

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