What sum of money will amount to 5200 in 6 years

Question 39 Compound Interest Exercise 14.2

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Answer:

Given details are,

Rate = 6 ½ % per annum = 13/2%

Simple Interest (SI) = Rs 5200

Time (t) = 2 years

By using the formula,

SI = (PTR)/100

P = (SI×100) / (T×R)

= (5200×100) / (2×13/2)

= (5200×100×2) / (2×13)

= 1040000/26

= Rs 40000

Now,

P = Rs 40000

R = 13/2% = 6.5%

T = 2years

By using the formula,

A = P (1 + R/100)^n

= 40000 (1 + 6.5/100)^2

= 40000 (106.5/100)^2

= Rs 45369

∴ CI = Rs 45369 – 40000 = Rs 5369

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A sum of money amounts to 5200 Rs. in 5 years and to 5680 Rs. in 7 years at simple interest. The rate of interest per annum is : [A]3% [B]4% [C]5% [D]6%

6% P + SI for 5 years = 5200…………(I) P + SI for 7 years = 5680…………(II) On subtracting equation (I) from (II) SI for 2 years = 480 ∴ SI for 1 years = 240 ∴ From equation (I), P + 5 $latex \times$ 240 = 5200 $latex => P = 5200 – 1200 = 4000 Rs.$ $latex \therefore R = \frac{SI\times 100}{T\times P}&s=1$ $latex = \frac{240\times 100}{1\times 4000} = 6\%&s=1$

Hence option [D] is correct answer.