Final answer:
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.