Question

Use the exponential growth model to calculate the amount of money you will have in the bank after 12 years if you deposit $31,000 into an account that pays 2.6% interest compounded continuously.

a) $42,513.63
b) $42,640.04
c) $42,235.18
d) $42,350.80

Answer 1

To find the amount of money after 12 years with continuous compounding at a 2.6% interest rate on a $31,000 principal, use the formula A = Pert. The calculation yields approximately $42,513.63, so the correct answer is (a) $42,513.63.

Step-by-step explanation:

To calculate the amount of money you will have in the bank after 12 years with a deposit of $31,000 in an account that pays 2.6% interest compounded continuously, you can use the formula for continuously compounded interest:

A = Pert

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• e is the base of the natural logarithm, approximately equal to 2.71828.
• r is the annual interest rate (decimal).
• t is the time the money is invested for, in years.

In this case:

• P = $31,000
• r = 0.026 (2.6% as a decimal)
• t = 12 years

Using the formula:

A = 31000e0.026 × 12

Calculating the value gives us:

A ≈ $42,513.63

Thus, after 12 years, you will have approximately $42,513.63 in the bank. So the answer is option (a) $42,513.63.