Question

If you invest $50 per day in an account earning an annual interest rate of 3.5%, how much will you have after 20 years?

Answer 1

With compound interest, the future value of one cash flow is given as under

Future value = Present value *(1+interest rate)^period

Here, cash is invested daily. The formula for future value of this savings annuity is as under

FV = d*((1+r/k)^Nk -1 )/(r/k)

Where FV is future value,

N is the number of years

d is regular periodic payment

r is interest rate per annum

k is number of compounding periods in a year

In this case, k will be 365 as dialy deposit is made.

Therefore, future value =

50*((1+0.035/365)^(20*365) - 1)/(0.035/365)

= 50*1.01367909/(0.035/365)

= 528,561.241

Thus, future value is $528,561.24.

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