## 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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