Find the future value, using the future value formula and a calculator. (Round your answer to the nearest cent.) $45.67 at 5.5% compounded daily for 3 years

Question

Find the future value, using the future value formula and a calculator. (Round your answer to the nearest cent.)

$45.67 at 5.5% compounded daily for 3 years

Answer 1

Generally speaking, interest rates in terms of years are used, so I suppose that 5.5% is the yearly interest rate. That would mean that the daily interest rate is 0.055/365 (ignoring leap years). So each day the value changes by a factor of 1 + 0.055/365.

There are 3*365 = 1095 days in three years. Therefore, the value changes by a factor of (1+0.055/365)^1095 over the course of three years. With initial value $45.67, in three years we will have:

$45.67*(1+0.055/365)^1095 = $53.8622

(Note that this is very close the value with continuously compounded interest, namely 45.67*exp(3*0.055)=53.8628.)

In general, with initial value V compounded daily at yearly interest rate r, the final value after n years would be given by the formula:

V(1+ r/365)^(365n)

Answer 2

The formula is FV = PV(1+i)^t with t in years and i as the annual rate written as a decimal (.055)

Plug it into calculator.