A loan of
$37,000
is made at
8.75%
interest, compounded annually. After how many years will the amount due reach
$93,000
or more?
37000*1.085^n = 93000
To calculate the number of years it will take for the loan amount to reach $93,000 or more, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (loan amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
From the given information, we know:
P = $37,000
r = 8.75% = 0.0875 (in decimal form)
A = $93,000
Since the interest is compounded annually, we have n = 1.
The formula can now be rewritten as:
$93,000 = $37,000(1 + 0.0875/1)^(1*t)
Next, we isolate t in the equation. Divide both sides of the equation by $37,000:
$93,000 / $37,000 = (1 + 0.0875/1)^(1*t)
Simplify the left side:
2.5135 = (1 + 0.0875)^t
To solve for t, we need to take the logarithm of both sides of the equation. Let's use the natural logarithm (ln):
ln(2.5135) = ln((1 + 0.0875)^t)
Using the logarithmic property, we can bring down the exponent:
ln(2.5135) = t * ln(1 + 0.0875)
Now, we can solve for t by dividing both sides of the equation by ln(1.0875):
t = ln(2.5135) / ln(1.0875)
Using a calculator or a computational tool, we can evaluate this expression to find the value of t. The calculated value of t will give us the number of years it will take for the loan amount to reach $93,000 or more.