If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum

1.	If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]
Answer» Amount invested = Rs. 10000 Interest rate = \(\frac8{100}=0.08\) amount after 1st year = 10000(1 + 0.08) = 10000(1.08) Value of the amount after n years = 10000(1.08) × (1.08)^n-1 = 10000(1.08)ⁿ = 20000 ∴ (1.08)ⁿ = 2 ∴ (1.08)⁵= 1.47 …..[Given] ∴ n = 10 years, (approximately)

If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]

Answer»

Amount invested = Rs. 10000

Interest rate = \(\frac8{100}=0.08\)

amount after 1st year = 10000(1 + 0.08)

= 10000(1.08)

Value of the amount after n years

= 10000(1.08) × (1.08)^n-1

= 10000(1.08)ⁿ

= 20000

∴ (1.08)ⁿ = 2

∴ (1.08)⁵= 1.47 …..[Given]

∴ n = 10 years, (approximately)