Question

find out the time by which a sum of Rs. 20000 fetches interest of Rs.7000 at 10% p.a.​

Answer 1

Answer:

Formula for compound interest is

A = P(1+r)^n

where,

A = compounded amount

P = principal

r = rate of interest

n = number of periods

Case 1 - Rs.20,000 invested for 2 years at 20% p.a. compounded yearly.

Since interest is compounded yearly rate of interest for year will be (20%) and number of periods will be (2 years). Hence, calculation will be done as follows.

A = 20000(1+0.2)^2

A = 20000(1.2)^2

A = 20000(1.44)

A = compounded amount = 28800

Case 2 - Rs.20,000 invested for 2 years at 20% p.a. compounded half-yearly.

Since interest is compounded half-yearly rate of interest for half year will be (20/2 = 10%) and number of half-years will be (2*2 = 4). Hence, calculation will be done as follows.

A = 20000(1+0.1)^4

A = 20000(1.1)^4

A = 20000(1.4641)

A = compunded amount = 29282

Difference in compounded amounts = 29282 - 28800 = 482

Hence, Rs.20,000 invested for 2 years at 20% p.a. for half-yearly compounding will earn Rs.482 more than when invested at yearly compounding.

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