Question

find the amount and the compound interest on 6500 for 2 years compounded annually the rate of interest being 5% per annum during the first year and 6% per annum during the second year?
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Answer 1

Solution :-

As we are provided :-

Principle Amount = 6500

Time period = 2 years

Rate of interest for first year = 5% per annum

Rate of interest for second year = 6% per annum

First of all as it have a variable rate of interest , hence we will find out the the Amount at the end of first year. Then it will be the Principle amount for next year.

As we know :-

$C.I. = P \left[\left( 1 + \dfrac{r}{100}\right)^t -1\right]$

Amount = C.I. + Principle Amount .

For first year :-

$C.I. = 6500 \left[\left( 1 + \dfrac{5}{100}\right)^1 -1\right]$

$C.I. = 6500\left[\left( \dfrac{105}{100}\right) -1\right]$

$C.I. = 6825 - 6500$

$C.I. = 325$

Now amount for second year = Principal amount + C.I.

= 6500 + 325

= 6825

Now for second year :-

$C.I. = 6825 \left[\left( 1 + \dfrac{6}{100}\right)^1 -1\right]$

$C.I. = 6825\left[\left( \dfrac{106}{100}\right) -1\right]$

$C.I. = \dfrac{723450}{100} - 6825$

$C.I. = 7234.5 - 6825$

$C.I. = 409.5$

Now total Compound Interest for both years :-

$= CI_{for\:year\:1} + CI_{for\:year\:2}$

= 325 + 409.5

= 734.5