Question

Application of exponential and logarithm functions. Round to hundredth.

You deposit $1000 in a bank account. If the account pays 3.5% annual interest compounded quarterly,
a) find the balance after 3 years.
b) how many years are needed to make the balance $5000

Answer 1

a) $1110.20

b) 46.18 years

Explanation:

We must apply the exponential formula for the calculation of annual compound interest problems

The formula is:

`P = P_0(1 + r) ^ t`

Where P is the profit after t years

`P_0` is the initial investment

r is the interest rate.

So in this problem, we have the quarterly interest rate.

We want to find the balance after 3 years. If in a year there are 4 quarters, then in 3 years there are t = 12 quarters.

a) To find the balance we substitute
`P_0 = 1000`,
`t = 12` quarters,
`r = (0.035)/(4)`

`P = 1000(1 + (0.035)/(4)) ^ {12}\\\\P = \$1110.20`

b) We must calculate t necessary to make the balance of 5000

`5000 = 1000(1 + (0.035)/(4)) ^ {4t}\\\\5 = (1 + (0.035)/(4)) ^ {4t}\\\\5 = (1.00875) ^ {4t}\\\\log(5) = 4tlog(1.00875)\\\\t = (log(5))/(4log(1.00875))\\\\t =\ 46.18 years`