Question

A certain loan program offers an interest rate of 7%, compounded continuously. Assuming no payments are made, how much would be owed after two years on a loan of $2500? Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

Answer:

The amount of loan after two years is $2875.68.

Explanation:

Given information:

Interest rate = 7%, compounded continuously.

Time = 2 years

Initial value of loan = $2500

The formula for amount after continuous compound interest is

$A=Pe^{rt}$

where,  P is principal,r is nominal rate per year, t is time in year.

Substitute P=2500, r=0.07, t=2 in the above formula.

$A=2500e^{0.07\cdot 2}$

$A=2500e^{0.14}$

$A=2875.68449714$

$A\approx 2875.68$

Therefore the amount of loan after two years is $2875.68.