A certain loan program offers an interest rate of
7%
, compounded continuously. Assuming no payments are made, how much would be owed after four years on a loan of
$3700
?
Do not round any intermediate computations, and round your answer to the nearest cent.
If necessary, refer to the
list of financial formulas
.
Using the formula for continuous compounding, we have:
A = P*e^(rt)
where A is the amount owed, P is the principal loan amount, r is the interest rate (as a decimal), and t is the time period.
Plugging in the given values, we get:
A = 3700*e^(0.07*4)
A = 3700*e^0.28
A = 5320.23
Therefore, the amount owed after four years is $5320.23.
To find the amount owed after four years on a loan with a continuous compounding interest rate of 7%, you can use the formula for compound interest:
Amount = Principal * e^(rate * time)
Where:
Principal = $3700 (loan amount)
Rate = 7% = 0.07 (as a decimal)
Time = 4 years
e = Euler's number (approximately 2.71828)
Plugging in the values into the formula:
Amount = 3700 * e^(0.07 * 4)
Calculating the exponent first:
0.07 * 4 = 0.28
Then, plugging it back:
Amount = 3700 * e^0.28
Using a calculator to find e^0.28:
e^0.28 ≈ 1.32313
Finally, multiply the result by the principal amount:
Amount = 3700 * 1.32313
Amount ≈ 4889.27
Therefore, the amount owed after four years on a loan of $3700, with a continuous compounding interest rate of 7%, would be approximately $4889.27.