A loan of 25,000 is made at 3.75% interest, compounded annually. After how many years will the amount due reach 42,000 or more?
25000(1.0375)^n = 42000
1.0375^n = 1.68
take logs of both sides and use rules of logs
n log 1.0375 = log 1.68
n = appr 14.09 years
To find the number of years it will take for the loan amount to reach $42,000 or more, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (42,000)
P = the initial loan amount (25,000)
r = the annual interest rate (3.75% written as a decimal, which is 0.0375)
n = the number of times interest is compounded per year (annually, so n = 1)
t = the number of years
Now, we can rearrange the formula to solve for 't':
t = (ln(A/P)) / (n * ln(1 + r/n))
Let's plug in the values:
t = (ln(42,000/25,000)) / (1 * ln(1 + 0.0375/1))
To solve this equation, we can use a scientific calculator or an online calculator. Taking the natural logarithm of (42,000/25,000) and dividing it by the natural logarithm of (1 + 0.0375/1), we get the answer:
t ≈ 9.607 years
Therefore, it will take approximately 9.607 years for the loan amount to reach $42,000 or more.