Hello My teacher skipped over this and I have no clue how to do this or the equations. Help would be wonderful thank you
If 6000 dollars is invested in a bank account at an interest rate of 10 per cent per year, find the amount in the bank after 15 years if interest is compounded annually
Find the amount in the bank after 15 years if interest is compounded quaterly
Find the amount in the bank after 15 years if interest is compounded monthly
Finally, find the amount in the bank after 15 years if interest is compounded continuously
annually: 6000(1+.1)^15 = 25,063.49
qly: 6000(1+.1/4)^(15*4) = 26,398.74
mly: 6000(1+.1/12)^(15*12) = 26,723.51
cont: 6000*e^(.1*15) = 26,890.13
What is the future value of $800 invested for 14 years at 11 percent compounded annually
To solve these types of problems, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount after time t
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Let's calculate the amounts using the given information:
1. Annual compounding:
In this case, n = 1 because the interest is compounded once a year.
Plugging the values into the formula:
A = 6000(1 + 0.10/1)^(1*15)
= 6000(1 + 0.10)^(15)
= 6000(1.10)^(15)
≈ $19,448.41
Therefore, the amount in the bank after 15 years with annual compounding will be approximately $19,448.41.
2. Quarterly compounding:
With quarterly compounding, n = 4 (as the interest is compounded 4 times a year).
We can now calculate using the formula:
A = 6000(1 + 0.10/4)^(4*15)
= 6000(1 + 0.10/4)^(60)
= 6000(1.025)^(60)
≈ $19,518.59
The amount in the bank after 15 years with quarterly compounding will be around $19,518.59.
3. Monthly compounding:
For monthly compounding, n = 12 (as interest is compounded 12 times a year).
Substituting the values into the formula:
A = 6000(1 + 0.10/12)^(12*15)
= 6000(1 + 0.10/12)^(180)
≈ $19,563.26
Therefore, the amount in the bank after 15 years with monthly compounding will be approximately $19,563.26.
4. Continuous compounding:
In the case of continuous compounding, we use the formula:
A = Pe^(rt)
where e is Euler's number, approximately 2.71828.
A = 6000 * e^(0.10*15)
= 6000 * e^(1.5)
≈ $19,569.86
Hence, the amount in the bank after 15 years with continuous compounding will be approximately $19,569.86.
Keep in mind that these are approximate values based on the provided information and simple interest calculations.