Question

Calculate the amount and compound interest on 17000 in 3 years when the rate of interest for successive years is 10%, 10% and 14% respectively.
A. 6578.70
B. 1700
C. 5489.8
D. 6449.80

Answer 1

Since three different rates of interests are given for the three years respectively, so we will use the formula for Amount.
And Interest will be the difference between Amount and Principal.

Complete step by step solution:
Now, according to the statement of the question, the Principal given is 17000, time is of 3years and the rate of interest for three years is 10% for first year, 10% for second year and 14% for third year.
So now according to the formula, the Amount is given as:

$A = P\left( {1 + \dfrac{{{r_1}}}{{100}}} \right)\left( {1 + \dfrac{{{r_2}}}{{100}}} \right)\left( {1 + \dfrac{{{r_3}}}{{100}}} \right)$

And the Interest will be calculated as: Interest = Amount – Principal
Now, first we will calculate the Amount as per the information in the question, using the formula given above:
So,
$\ P = Rs.17000 \\\ {r_1} = 10\% ,{r_2} = 10\% ,{r_3} = 14\% \\\ t = 3years \\\ \$
Then the amount will be:
$\ A = 17000\left( {1 + \dfrac{{10}}{{100}}} \right)\left( {1 + \dfrac{{10}}{{100}}} \right)\left( {1 + \dfrac{{14}}{{100}}} \right) \\\ = 17000\left( {\dfrac{{100 + 10}}{{100}}} \right)\left( {\dfrac{{100 + 10}}{{100}}} \right)\left( {\dfrac{{100 + 14}}{{100}}} \right) \\\ = 17000\left( {\dfrac{{110}}{{100}}} \right)\left( {\dfrac{{110}}{{100}}} \right)\left( {\dfrac{{114}}{{100}}} \right) \\\ = 17000\left( {\dfrac{{11}}{{10}}} \right)\left( {\dfrac{{11}}{{10}}} \right)\left( {\dfrac{{114}}{{100}}} \right) \\\ = \dfrac{{17 \times 11 \times 11 \times 114}}{{10}} \\\ = 23449.8 \\\ \$
Therefore, the Amount is 23449.8
$\ Interest = Amount - Principal \\\ = 23449.80 - 17000 \\\ = 6449.80 \\\ \$

So, after 3 years the total amount earned is 23449.80 while the total interest earned is 6449.80

Therefore, the total interest earned in 3 years is 6449.80

Hence, the correct option is option D.

Note: The calculations of amount have to be done very carefully, even a single small mistake in a single digit will give us a different and wrong answer.