Final answer:
Using the compound interest formula, Jennifer's $50,000 investment at a 15% annual interest rate will grow to approximately $202,277.50 after 10 years.
Step-by-step explanation:
Calculating Future Value with Compound Interest
Jennifer's initial investment is $50,000 and it grows at a rate of 15% annually. To calculate how much money she will have after 10 years, we use the formula for compound interest:
A = P(1 + r/n)(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In Jennifer's case, since the interest is compounded annually (once per year), the value of n is 1. Thus, the formula simplifies to:
A = $50,000(1 + 0.15)10
We can now calculate the future value of Jennifer's investment:
A = $50,000(1 + 0.15)10
= $50,000(1.15)10
= $50,000(4.04555...)
= $202,277.50 approximately
Therefore, after 10 years, Jennifer's investment would have grown to approximately $202,277.50.