Final answer:
The value of Thatcher's investment after 5 years, given a 4% interest rate compounded quarterly, is $6955.08. This uses the compound interest formula A = P(1 + r/n)^(nt), where A is the accumulated amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years.
Step-by-step explanation:
To determine the value of Thatcher's investment after 5 years in an annuity with a 4% interest rate, compounded quarterly, we use the formula for compound interest:
A = P(1 + rac{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.
Given Thatcher's investment details, we have:
- P = $5700
- r = 4% or 0.04
- n = 4 (quarterly)
- t = 5 years
Plugging these into the formula we get:
A = 5700(1 + rac{0.04}{4})^{4 imes 5}
A = 5700(1 + 0.01)^{20}
A = 5700(1.01)^{20}
A = 5700 imes 1.21939
A = $6955.08
Therefore, the value of Thatcher's investment after 5 years is $6955.08, which matches option d.