Dolores Invest $8500 in a new savings account which owns 3.1% annual interest, compounded daily. What will be the value of her investment after three years?
i = .031/365 = ....
n = 365*3 = ...
sub into :
amount = 8500(1+i)^n
Well, Dolores is certainly making a "savings"ious decision! Let me calculate that for you.
Using the compound interest formula, the value of her investment after three years can be calculated as:
V = P(1 + r/n)^(nt)
Where:
V is the value of the investment after three years,
P is the principal (initial investment) of $8500,
r is the annual interest rate of 3.1% (or 0.031 as a decimal),
n is the number of times the interest is compounded per year (in this case, daily, so n = 365),
and t is the number of years (three years).
Plugging in the values, we get:
V = 8500(1 + 0.031/365)^(365*3)
Calculating all that, the value of Dolores' investment after three years would be approximately $9,207.97.
Looks like Dolores' savings account is growing faster than the jokes at a clown convention!
To calculate the value of the investment after three years, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case:
P = $8500
r = 3.1% or 0.031 (decimal form)
n = 365 (compounded daily)
t = 3 years
Plugging these values into the formula:
A = 8500(1 + 0.031/365)^(365*3)
Calculating the exponent first:
A = 8500(1.0000849315068493150684931506849)^(1095)
Then, raising the base to the exponent:
A ≈ 8500 * 1.096184139223272063893456699793
Finally, calculating the future value:
A ≈ $9317.56
Therefore, the value of Dolores' investment after three years will be approximately $9317.56.
To calculate the value of Dolores' investment after three years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (the value of the investment after three years)
P = the principal amount (the initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, Dolores invested $8500 at an annual interest rate of 3.1% compounded daily, so:
P = $8500
r = 3.1% (or 0.031 as a decimal)
n = 365 (since interest is compounded daily)
t = 3 years
Now we can substitute these values into the formula and calculate the amount:
A = 8500(1 + 0.031/365)^(365*3)
To simplify the equation, we can calculate the daily interest rate by dividing the annual interest rate by the number of days in a year:
daily interest rate = 0.031 / 365
Now we can substitute this value into the formula:
A = 8500(1 + (0.031/365))^(365*3)
Calculating this equation will give us the final value of Dolores' investment after three years.