Question

Rhonda deposits $5,600 in a savings account that pays 1.5% interest, compounded semi-annually.

Round to the nearest cent.

Answer 1

Part a)
`\$42`

Part b)
`\$5,642`

Part c)
`\$42.32`

Part d)
`\$5,684.32`

Part e)
`\$84.32`

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

`A=P(1+(r)/(n))^(nt)`

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

`t=6/12=0.5\ years\\ P=\$5,600\\ r=1.5\%=1.5/100=0.015\\n=2`

substitute in the formula above

`A=5,600(1+(0.015)/(2))^(2*0.5)`

`A=5,600(1.0075)^(1)`

`A=\$5,642`

Find out the interest

`I=A-P`

`I=\$5,642-\$5,600=\$42`

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

`A=\$5,642` ----> see part a)

Part c) How much interest does the account earn in the second 6 months?

in this part we have

`t=6/12=0.5\ years\\ P=\$5,642\\ r=1.5\%=1.5/100=0.015\\n=2`

substitute in the formula above

`A=5,642(1+(0.015)/(2))^(2*0.5)`

`A=5,642(1.0075)^(1)`

`A=\$5,684.32`

Find out the interest

`I=A-P`

`I=\$5,684.32-\$5,642=\$42.32`

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

`\$5,600+\$42+\$42.32=\$5,684.32`

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

`\$42+\$42.32=\$84.32`