Question

Please Do NOT USE excel to solve .... Show me the steps and the equations to better understand the question

You have a habit of drinking a cup of coffee ($2.00 a cup) on the way to work every morning for 30 years. If you put the money in the bank for the same period, how much would you have, assuming your accounts earns 5% interest compounded daily. a) If we would like to use N=30 years, Find the equivalent interest (per year) b) Find Future Sum at N=30 years.

Answer 1

Given, APR = 5% p.a. compounded daily.

a). So, Equivalent interest rate per year = (1 + APR/n)^n - 1 = (1 + 0.05/365)^365 - 1 = 5.13% per year.

b). if rs 2 is deposited daily for next 30 years, Future sum can be calculate using formula

FV = PMT*((1+r/n)^(t*n) - 1 )/(r/n) = 2*(1+0.05/365)*((1+0.05/365)^(365*30) - 1)/(0.05/365) = $50832.90