Final answer:
The total amount after 19 years is $104,946.23 (Option E). This is calculated by using the compound interest formula A = P(1 + r/n)^(nt), with P = $12,500, r = 13.3%, n = 4, and t = 19 years.
Step-by-step explanation:
The question asks us to calculate the future value of a $12,500 deposit invested at an annual interest rate of 13.3% with quarterly compounding over a period of 19 years.
To solve this, we will use the formula for compound interest:
A = P(1 + r/n)(nt)
Where:
- A = the amount of money accumulated after n years, including interest.
- P = the principal amount (the initial amount of money).
- r = the annual interest rate (decimal).
- n = the number of times that interest is compounded per year.
- t = the time the money is invested in years.
Substituting the given values into the formula:
A = $12,500(1 + 0.133/4)(4*19)
Calculating this gives us:
A = $12,500(1 + 0.03325)76
Which simplifies to:
A = $12,500(1.03325)76
After using a calculator, the final answer is:
A ≈ $104,946.23
Hence, the correct answer is $104,946.23 (Option E).
The complete question is: If a $12,500 deposit is invested at an annual interest rate of 13.3% with quarterly compounding, what is the total amount after 19 years?
a) $45,768.72
b) $34,125.50
c) $23,980.15
d) $15,932.60
e) $104,946.23.