Final answer:
The approximate time for a loan of $16,120 at 5% interest, compounded annually, to reach $18,300 is 2.60 years; thus, the closest answer is B) 3 years.
Step-by-step explanation:
To find the approximate time it takes for a loan of $16,120 at 5% interest, compounded annually, to reach an amount due of $18,300, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
In this problem, A=$18,300, P=$16,120, r=0.05 (since 5% as a decimal is 0.05), and n=1 (since the interest is compounded annually).
To find t, we rearrange the formula to solve for t and get:
t = log(A/P) / (n*log(1+r/n))
Substituting the values, we have:
t = log(18300/16120) / (1*log(1+0.05/1))
t = log(1.13546) / log(1.05)
t = 0.05512 / 0.02119
t ≈ 2.60 years
Therefore, the closest answer is B) 3 years.