MODELING REAL LIFE

Question

You deposit $50 in an investment account that earns 7% annual interest compounded monthly. Write a function m that represents the balance (in dollars) of the investment account after t years

What is the balance after 3 years?

Answer 1

The equation for compounded interest is:

M(t) = M₀·(1 + r/n)^nt

where:

1. M(t) = the amount of money in the account after t years
2. M₀ = the initial amount = $50
3. r = interest rate (7%) expressed as a decimal = 0.07
4. n = number of compoundings per year = monthly = 12
5. t = years

Plug the values into the equation above to get you specific function M(t). For the balance after 3 years, set t = 3 and use your calculator to compute the answer.

Answer 2

Answer 3

Compound Interest

A = P(1+r/n)^nt

P = Principal/Initial Value = $50

r = Interest Rate = 7% (per year) = 0.07

n = Number of Times Interest Applied During Time Period = 12 (months)

t = Number of Times Period Elapsed = 3 (years)

Evaluate

A = P(1+r/n)^nt = 50(1+0.07/12)^12•3 ≈ $61.65

Hence, the balance after 3 years will be about $61.65

Hope this helped!