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Maths-

General

Easy

Question

Mr. utter invested Rs5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs5325. Calculate (i) The rate of interest (ii) The amount at the end of the second year, to the nearest rupee.

hint Hint:

Use the formula of total amount to find the rate of interest and from that find amount at the end of second year.

The correct answer is: 5671 Rupees

Complete step by step solution:
(i) We calculate the total amount by the formula $A equals P open parentheses 1 plus R over 100 close parentheses to the power of T$ …(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 1 years, P = 500, A = 5325 and R = ?
On substituting the known values in (i), we get $5325 equals 5000 open parentheses 1 plus R over 100 close parentheses to the power of 1$
On dividing both the sides by 5000, we have 1.065 = $open parentheses 1 plus R over 100 close parentheses to the power of 1$
$not stretchy rightwards double arrow 0.065 cross times 100 equals R$
$not stretchy rightwards double arrow R equals 6.5 straight percent sign$
(ii) By the end of first year principal amount becomes, P = 5325 Rupees
We calculate amount at the end of second year by the formula $A equals P open parentheses 1 plus R over 100 close parentheses to the power of T$ …(ii)
Here, we have T = 1 years, P = 5325, R = 6.5 and A = ?
On substituting the known values in (ii), we get $A equals 5325 open parentheses 1 plus fraction numerator 6.5 over denominator 100 end fraction close parentheses to the power of 1$
$not stretchy rightwards double arrow A equals 5325 cross times 1.065 equals 5671.125$
$not stretchy rightwards double arrow A equals 5671$ Rupees(approx)
Hence the amount at end of second year = 5671 Rupees

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