Answer:
Part a) [tex]\$42[/tex]
Part b) [tex]\$5,642[/tex]
Part c) [tex]\$42.32[/tex]
Part d) [tex]\$5,684.32[/tex]
Part e) [tex]\$84.32[/tex]
Step-by-step explanation:
The complete question is
Rhonda deposits $5,600 in a savings account that pays 1.5% interest, compounded semi-annually. Round to the nearest cent.
a. How much interest does the account earn in the first 6 months?
b. What is the ending balance after 6 months?
c. How much interest does the account earn in the second 6 months?
d. What is the balance after 1 year?
e. How much interest does the account earn the first year?
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part a) How much interest does the account earn in the first 6 months?
in this part we have
[tex]t=6/12=0.5\ years\\ P=\$5,600\\ r=1.5\%=1.5/100=0.015\\n=2[/tex]
substitute in the formula above
[tex]A=5,600(1+\frac{0.015}{2})^{2*0.5}[/tex]
[tex]A=5,600(1.0075)^{1}[/tex]
[tex]A=\$5,642[/tex]
Find out the interest
[tex]I=A-P[/tex]
[tex]I=\$5,642-\$5,600=\$42[/tex]
Part b) What is the ending balance after 6 months?
we know that
The ending balance after 6 months is the same that the final investment value of A after 6 months
so
[tex]A=\$5,642[/tex] ----> see part a)
Part c) How much interest does the account earn in the second 6 months?
in this part we have
[tex]t=6/12=0.5\ years\\ P=\$5,642\\ r=1.5\%=1.5/100=0.015\\n=2[/tex]
substitute in the formula above
[tex]A=5,642(1+\frac{0.015}{2})^{2*0.5}[/tex]
[tex]A=5,642(1.0075)^{1}[/tex]
[tex]A=\$5,684.32[/tex]
Find out the interest
[tex]I=A-P[/tex]
[tex]I=\$5,684.32-\$5,642=\$42.32[/tex]
Part d) What is the balance after 1 year?
we know that
The balance after 1 year is equal to the initial deposit of $5,600 plus the interest earned in the first 6 months plus the interest earned in the second 6 months
so
[tex]\$5,600+\$42+\$42.32=\$5,684.32[/tex]
Part e) How much interest does the account earn the first year?
The total interest the first year is equal to the interest earned in the first 6 months plus the interest earned in the second 6 months
so
[tex]\$42+\$42.32=\$84.32[/tex]
