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1
A certain sum amounts to INR 16590 in
4
2 years at 8.5% p.a. at simple interest. The same sum amounts to
INR x in 2 years at 15% p.a. when the interest is compounded 8-monthly. The value of x is:
15792
R15927
15972
100921016
102921016
15752​

Answer 1

Answer:

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Answer 2

The value of x is 15,972

Given - Amount, rate of interest and time

Find - Value of x

Solution - We will be using three formulas to find the value of x. First we will find principal amount from values given about simple interest. Then, we will find the amount of compound interest from the obtained principal amount.

Amount = Principal + Interest

16590 = P + I

I = 16590 - P

SI = PRT÷100

Keep the value of interest in formula -

16590 - P = P×8.5×4.5÷100

Performing multiplication on Right Hand Side

1659000 - 100P = 38.25P

Shifting 100P to Right Hand Side and performing addition

138.25P = 1659000

Shifting the value on Right Hand Side and performing division

P = 12000

Formula for calculation of amount through compound interest

n = 12÷8

n = 1.5

A =${ P (1 + r÷n)}^{nt}$

Keep the values in formula

x = ${P(1 + \frac{0.15}{1.5} )}^{1.5 \times 2}$

Performing multiplication in power

x = ${12000(1 + \frac{0.15}{1.5} )}^{3}$

Solving the bracket

x = ${12000(1.1)}^{3}$

Taking power of values in bracket

$x = 12000 \times 1.331$

Performing multiplication

x = 15,972

Hence, the value of x is 15,972

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