Question

An initial investment of $350 is worth $429.20 after six years of continuous compounding. Find the

annual interest rate.

Answer 1

To find the annual interest rate, we use the formula for continuous compound interest and solve for r. After plugging in the given values, we find that the annual interest rate is approximately 3.7%.

Step-by-step explanation:

To find the annual interest rate, we need to use the formula for continuous compound interest:

A = P * e^(rt)

where A = final amount, P = initial investment, r = annual interest rate, and t = time in years. We are given that P = $350, A = $429.20, and t = 6 years. Plugging in these values, we get:

$429.20 = $350 * e^(6r)

Dividing both sides by $350, we get:

e^(6r) = $429.20 / $350

Taking the natural logarithm of both sides, we get:

ln(e^(6r)) = ln($429.20 / $350)

Using the property of natural logarithm, the exponent comes down as a coefficient and we have:

6r = ln($429.20 / $350)

Dividing both sides by 6, we get:

r = ln($429.20 / $350) / 6

Now we can use a calculator to find the value of r, which is approximately 0.037 or 3.7%.

Answer 2

Interest Rate : 0.0346 or 3.46%

Step-by-step explanation:

• 429.2=350*(1+x)^6

• 429.2/350= (1+x)^6

•(429.2/350)^(1/6)= 1+x

•(429.2/350)^(1/6)-1= x

Check work:

350*(1+0.0346)^6=429.2