Question

How long will it take an amount to double if it is deposited into an account which pays 3.8% interest compounded continuously? Use a 360 day year and give the answer to the nearest day.

Please show work. I am willing to rate you well if you give in-depth detail as how to solve the problem. Thanks!

Answer 1

Let's say initial amount (PV) deposited is $1

Future value (FV) = $2 i.e double of PV

Interest rate (i), continuous compounding = 3.8%

and we need to find time(n) that it will take make initial amount double.

As question required, we have calculate time in days, thus convert interest rate to daily interest rate.

Daily interest rate(i) = 3.8%/360 = 0.0105555555%

We can calculate Time(n) by putting values in Future value equation (continuous compounding) :-

take natural log both side

..... ( ln(e) = 1)

Thus, it will take 6,567 days to double the amount.