Final answer:
To find out how long it will take for Donald to have $4500 in his savings account with a 3% interest rate compounded monthly, we can use the formula for compound interest. After solving the equation, we find that it will take around 5 years for Donald to have $4500 in his account.
Step-by-step explanation:
To find out how long it will take for Donald to have $4500 in his savings account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial deposit), r is the interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years.
Let's plug in the values: A = $4500, P = $720, r = 3% = 0.03, and n = 12 (since interest is compounded monthly). We need to solve for t:
$4500 = $720(1 + 0.03/12)^(12t)
Divide both sides by $720 and simplify the right side of the equation:
6.25 = (1 + 0.0025)^(12t)
Take the natural logarithm of both sides to isolate t:
ln(6.25) = ln((1 + 0.0025)^(12t))
Use logarithm properties to bring down the exponent:
ln(6.25) = 12t * ln(1 + 0.0025)
Divide both sides by 12 * ln(1 + 0.0025) and solve for t:
t = ln(6.25) / (12 * ln(1 + 0.0025))
Calculate the value of t using a calculator:
t ≈ 5.62
Therefore, it will take approximately 5 years for Donald to have $4500 in his savings account.