Respuesta :
Answer:
Uptown industries have to deposit today $4,145.
Explanation:
To find the final capital at the end of the third year, we use the compound interest formula:
Final Capital (FC)= Initial Capital (IC)*[(1+interest(i))]^(number of periods(n))
FC=$3000*[1+2.75%]^(12)
FC= $4,145.35
Then, Uptown industries have to deposit today $4,145.
Uptown businesses must deposit $4,154 today to have the same amount saved at the end of three years.
What is compound interest?
The adding of interests to the payment of principal of borrowing or deposit is known as compound interest.
The original loan, or principal, is multiplied by one plus the yearly interest rate increased to the numbers of compounding periods minus one to determine compound interest.
[tex]A =[P (1 + r/100)^{n}][/tex]
Where:
A = the investment/future loan's worth, including interest
The principal investment or initial amount is denoted by the letter P.
The yearly interest rate is denoted by the letter r.
The number of times interest is compounding per year is referred to as n.
[tex]\text{Final Capital} (FC)= \text{Initial Capital}(IC)\times [{(1+\frac{r}{100})^{n}][/tex]
In this case, we have to calculate the amount that has to be deposited to get the capital at the conclusion of the third year:
[tex]FC= \$3,000 [1+2.75/100] ^{12} \\FC= \$3,000 [1+2.75/100]^{12} \\FC=\$3,000 [1+ 0.275]^{12} \\FC= \$3,000 [ 1.38478]\\FC= \$4,154[/tex]
Hence, uptown Industries must deposit $4,154 today to have the same amount saved at the end of the three years if the interest is compounded quarterly.
To learn more about compound interest, refer to the link:
https://brainly.com/question/24274034
