An amount of 234000 is deposited in a bank paying an annual

An amount of $2,340.00 is deposited in a bank paying an annual interest rate of 3.1%, compounded continuously. Find the balance after 3 years.

Determine the amount compounded continuously on an annual basis?

Deternime the amount compounded continuously on a quarterly basis?

Solution

1. The formula, where the interest is continuously compounded is F = Pe^rt, where F is the future value, P is the present value, r is the rate of interest in decimals and t is the number of years.

Here, P = $2340, r = 3.1/100 = 0.031, and t = 3. Then F = 2340*e^0.031*3 = 2340*e^0.093 = 2340*1.097461735 = $ 2568.06 ( on rounding off to the nearest cent).

2. The formula, where the interest is compounded on quarterly basis is F = P(1+r/4)^4t, where F is the future value, P is the present value, r is the rate of interest in decimals and t is the number of years. Here, $2340, r = 3.1/100 = 0.031, and t = 3.Then F = 2340*( 1+0.031/4)^4*3 = 2340*(4.031/4)¹² = 2340*(1.00775)¹²= 2340*1.09706834 = $ 2567.14( on rounding off to the nearest cent).