Final answer:
To find out how many years it will take for the loan amount to reach $48,000 or more, we can use the formula for compound interest.
Step-by-step explanation:
To find out how many years it will take for the loan amount to reach $48,000 or more, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount due after t years
P = the principal loan amount
r = the annual nominal interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the time in years
In this case, we have:
P = $28,000
A = $48,000
r = 6.25% = 0.0625
n = 1 (compounded annually)
Substituting these values into the formula, we have:
$48,000 = $28,000(1 + 0.0625/1)^(1t)
Dividing both sides of the equation by $28,000, we get:
1.7143 = (1.0625)^t
Next, we can take the natural logarithm of both sides of the equation to solve for t:
t = ln(1.7143)/ln(1.0625)
Using a calculator, we find that t ≈ 7.99 years. Therefore, it will take approximately 8 years for the loan amount to reach $48,000 or more when the interest is compounded annually at a rate of 6.25%.