If Joanie puts \(\$500\) in a savings account that earns \(10\) percent annual interest compounded semiannually, how muc

[M7MBA]

If Joanie puts \(\$500\) in a savings account that earns \(10\) percent annual interest compounded semiannually, how much money will be in the account after one year?

A) \(\$51.25\)
B) \(\$510\)
C) \(\$550\)
D) \(\$551.25\)
E) \(\$565\)

Answer: D

Source: Princeton Review

[deloitte247]

For compound interest;
$$A=P\left(1+\frac{r}{n}\right)^{^{nt}}$$
Where A = final amount; P = initial principal; r = interest rate
n = no. of times interest compounded; t = no. of time period elapsed
P = $500
Since the money is compounded semi-annually,
r = 10 * 1/2 = 5%
t = 1*2 = 2
n = 1
$$A=500\left(1+\frac{5\%}{1}\right)^{^{1\cdot2}}$$
$$A=500\left(1+0.05\right)^{^2}$$
$$A=500\left(1.05\right)^{^2}$$
$$A=500\cdot1.05\cdot1.05=$551.25$$

[Scott@TargetTestPrep]

If Joanie puts \(\$500\) in a savings account that earns \(10\) percent annual interest compounded semiannually, how much money will be in the account after one year?

A) \(\$51.25\)
B) \(\$510\)
C) \(\$550\)
D) \(\$551.25\)
E) \(\$565\)

Answer: D

Solution:

We use the compound interest formula: A = P (1 + r/n) ^ nt, where P is $500, r = 0.10, n = 2 (because of semi-annual interest), and t = 1.

Thus, after one year, Joanie has:

500(1 + 0.1/2)^2 = 500(1.05)^2 = 500(1.1025) = $551.25

Answer: D