Alicia Eastman deposited $2,000 in a savings account at the Biltmore Bank paying 6% ordinary interest. How many years will it take for her investment to amount to $2,600?
Using the scenario from the previous question, determine the maturity date of the loan.
I - PRT
600 = 2000 * 0.06 * T
600 = 120T
600 / 120 = T
? = T
t=5
To determine the number of years it will take for Alicia Eastman's investment to amount to $2,600, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($2,600 in this case)
P = the principal amount (initial deposit of $2,000)
r = the annual interest rate (6% or 0.06)
n = the number of times interest is compounded per year (assuming annual compounding, n = 1)
t = the number of years
We need to solve for t.
2,600 = 2,000(1 + 0.06/1)^(1*t)
Simplifying the equation:
2,600 = 2,000(1.06)^t
Now we can solve for t by rearranging the equation:
(1.06)^t = 2,600/2,000
Using a calculator, we find:
(1.06)^t ≈ 1.3
Next, take the logarithm of both sides of the equation to isolate t:
ln((1.06)^t) ≈ ln(1.3)
Using natural logarithm (ln):
t * ln(1.06) ≈ ln(1.3)
Divide both sides of the equation by ln(1.06) to solve for t:
t ≈ ln(1.3) / ln(1.06)
Using a calculator to compute the natural logarithms, we find:
t ≈ 0.262364 / 0.058268 ≈ 4.508
Therefore, it will take approximately 4.508 years for Alicia Eastman's investment to amount to $2,600.
For the second question, the maturity date of the loan cannot be determined based on the given information. The maturity date would depend on the terms and conditions set by the Biltmore Bank, such as the length of the loan period, repayment schedule, and any additional terms. More information is needed to determine the maturity date of the loan.
To answer the first question, we can use the formula for calculating simple interest:
Interest = Principal * Rate * Time
In this case, Alicia deposited $2,000 in a savings account with a 6% interest rate. We want to find out the time it will take for her investment to amount to $2,600. Let's call this unknown time "t".
We can rearrange the formula to solve for time:
Time = Interest / (Principal * Rate)
Here, the interest is the difference between the final amount ($2,600) and the principal amount ($2,000), which is $600.
Plugging in the values into the formula:
t = 600 / (2000 * 0.06)
Simplifying the equation:
t = 600 / 120
t = 5
Therefore, it will take Alicia 5 years for her investment to amount to $2,600 in her savings account at the Biltmore Bank.
Now, to answer the second question about determining the maturity date of the loan, we need more information about the loan. Specifically, we need to know the loan principal, the interest rate, and the term (duration) of the loan. Once we have this information, we can calculate the maturity date using the start date of the loan and the term.