Answer to Question #217121 in Financial Math for Ankur anegi

Question

Mohit deposited Rs. 1,00,000 in a bank for 3 years offering interest rate of 6% 

compounded half- yearly during first year, at the rate of 12% compounded quarterly 

during second year and at 10% compounded continuously during third year. Find his 

balance after 3 years. 

Answer 1

$The \ principal \ amount \ is \ Rs.1,00,000\\ Rate \ of \ interest \ is \ 6For \ the \ first \ year \ compounded \\ half yearly.\\ \Rightarrow Amount \ after \ one \ year \ is \ A= 100000(1+\frac{6}{200})^{2}\\ =100000(1.03)^{2}\\ =100000(1.0609)\\ =106090\\ The \ amount \ after \ one \ year \ is \ A= Rs.1,06,090\\ The \ rate \ of \ interest \ in \ the \ second \ year \ is \ 12Since \ the \ interest\ is \ compunded \ quartely\ the \ amount \ at \ the \ end \ of \ second \ year \ is \ A= 106090(1+\frac{12}{400})^{4}\\since \ in \ an \ year\ there \ are \ 4 \ quarters\\ =106090(1.03)^{4}\\ =106090(1.12550881)\\ =119405.23\\ For \ the \ 3rd \ year \ the \ interest \ is 10\Rightarrow \ 119405.23(e)^{(0.1)(1)}=119405.23(e^{0.1})=131963.19\\ Therefore, the \ amount \ after \ 3 \ years \ is \ A = Rs.131963.19$