Question

The compound interest on a certain sum for 2and1/2 years at 5% per annum compounded annually is 416.20
find the sum
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Answer 1

Answer:

368.4078

Step-by-step explanation:

Let the sum invested be denoted by $x$

Year One:

At the beginning we have $x$

Interest earned in year 1 is

$\frac{5}{100}*x=0.05x$

The total amount at the end of the year is

$x+0.05x=1.05x$

Year Two:

At the beginning we have $1.05x$

Interest earned is given by

$\frac{5}{100}*1.05x=0.0525x$

The total amount at the end of the year is

$1.05x+0.0525x=1.1025x$

Year Three:

At the beginning we have $1.1025x$

This amount compounded to the middle of the year becomes

$Amount=1.1025x*(1+\frac{5}{100})^{0.5)\\ Amount=1.129726322x$

Equating this to the actual amount we get;

$1.129726322x=416.20x=368.4078099$