Respuesta :
Answer: $1,126.16
Explanation:
Given that,
Amount deposited in savings account = $1,000
Interest rate = 8%, compounded quarterly
Since the interest is compounded quarterly, therefore
[tex]Number\ of\ periods = \frac{18}{3}[/tex]
n= 6
[tex]Effective\ rate\ of\ interest=\frac{Interest\ Rate}{4}[/tex]
[tex]Effective\ rate\ of\ interest=\frac{0.08}{4}[/tex]
= 0.02
e = 2%
Hence,
[tex]Amount\ to\ be\ received = Deposited\ Amount\times(1+e)^{n}[/tex]
[tex]Amount\ to\ be\ received = 1,000\times(1+0.02)^{6}[/tex]
= 1,000 × 1.1261
= $1,126.16
The sum of money that will be received after 18 months is $1,126.16. The sum is received after compounding the principal for 18 months at a rate 8%.
What is compounding?
Compounding refers to the process in which the interest is credited on the principal amount as well as on the interest up-to the date of interest calculation.
The formula to calculate the amount after compounding is:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
where A is the final amount, P is the principal, r is the rate of interest, n is the number of times principal is compounded in a year, and t is the tenure (in years).
Given:
Principal is $1,000
Rate is 8%
Compounding is quarterly therefore n will be 4.
And the value of t is the tenure, that is 18 months or 1.5 years.
Therefore the amount will be:
[tex]\rm A = 1000(1+\dfrac{0.08}{4})^{4\times1.5}\\\\\rm A = 1000(1.02)^{6}\\\\\rm A = 1000(1.126)\\\\\rm A = \$1,126.16[/tex]
Therefore the amount we will receive is $1,126.16
Learn more about compounding here:
https://brainly.com/question/2883618
