Respuesta :

calculista

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]

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