Question

If an employee deposits Rs. 2,000 at the end of each year into his company’s plan which pays 7% interest compounded quarterly, how much will he have in the account at the end of 5 years?

Answer 1

The interest is compounded quarterly, with a year total of 7%. This means that effectively 7/4 = 1.75% a paid every quarter, leading to a year total interest of $1.0175^4 - 1=0.071859$

If the employer starts his first year with $Sum_i = 2000$ on his account then on the end of first year he will have

$$Sum_1=2000+Sum_i*0.071859+Sum_i=2000+1.071859 *Sum_i=4143.718$$

For the year 2 the situation is analogous

$$Sum_2=2000+1.071859 *Sum_2 = 2000+1.071859*4143.718= 6441.48$$

For the end of year 3 and 4

$$Sum_3=2000+1.071859 *Sum_2 = 2000+1.071859*6441.48= 8904.36$$ $$Sum_4=2000+1.071859 *Sum_3 = 2000+1.071859*8904.36= 11544.22$$

and finally an employee will have

$$Sum_5=2000+1.071859 *Sum_4 = 2000+1.071859*11544.22= 14373.78$$

Rs. in his account.