Please help:
A continuously compounded account starts with $2500 in principal. The annual interest rate is 11.3%. What is the balance after 15 years?
pert:
Value= Principal*ert
= 2500* e0.11(15)
= 2500 * e1.65
wow.
thanks
To calculate the balance after 15 years in a continuously compounded account, you can use the formula:
Value = Principal * e^(rt)
Where:
- Principal is the initial amount (in this case, $2500)
- e is the base of the natural logarithm, approximately 2.71828
- r is the annual interest rate expressed as a decimal (in this case, 11.3% or 0.113)
- t is the number of years (in this case, 15)
So, plugging in the values:
Value = 2500 * e^(0.113 * 15)
To calculate this with a calculator, you can follow these steps:
1. Take the annual interest rate (11.3%) and convert it to a decimal by dividing by 100. So, 11.3% = 0.113.
2. Multiply the rate by the number of years (15): 0.113 * 15 = 1.695.
3. Now, take e^(1.695) using a scientific calculator. On most calculators, you can find the "e^x" or "exp(x)" function.
4. Multiply the result by the principal amount ($2500):
Value = 2500 * e^(1.695)
Calculating this using the values mentioned above, the balance after 15 years would be approximately $7,038.09.