Compound Interest Mathematical Problem

Question: A Person has invested Rs. 10000 in a bank at an interest of 10% per annum. How much amount will receive After 2 years if the compounding is done?

a) Annually.
b) Semi-Annually.
c)Quarterly.
d)Monthly.
e)Daily

Answer:

FV_n = PV ( 1+ ^r/_m )^mn

Where, FVn = Future value after n years

n = Number of years [In the above math, n = 2]

m = Number of times compounding is done in a year

a) Annually.

Here, r = 0.10 (10%), m = 1.

FV = PV ( 1+ ^0.10/₁ )^1×2 = 10000(1+0.10)²= 10000 × (1.10)² = 12100 Rs.

b) Semi-Annually.

Here, r = 0.10 (10%), m = 2.

FV = PV ( 1+ ^0.10/₂ )^2×2 = 10000(1+0.05)⁴= 10000 × (1.05)⁴ = 12155 Rs.

c) Quarterly.

Here, r = 0.10 (10%), m = 4.

FV = PV ( 1+ ^0.10/₄ )^4×2 = 10000(1+0.025)⁸= 10000 × (1.025)⁸ = 12184 Rs.

d) Monthly.

Here, r = 0.10 (10%), m = 12.

FV = PV ( 1+ ^0.10/₁₂ )^12×2 = 10000(1+0.0083)²⁴= 10000 × (1.0083)²⁴ = 12194 Rs.

e) Daily

Here, r = 0.10 (10%), m = 365.

FV = PV ( 1+ ^0.10/₃₆₅ )^365×2 = 10000(1+0.000274)⁷³⁰= 10000 × (1.000274)⁷³⁰ = 12214 Rs.

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