Marisa invests $1650 for 3 years, at which time her investment is worth $2262.7. What interest rate , compounded annually, would yield the same results? Found your answer to 2 decimal places.
1650(1+i)^3 = 2262.7
divide both sides by 1650, take the cube root, then subtract 1 to get i, the annual rate expressed as a decimal.
let me know what you got.
If 2 years ago, Mike placed $500,000.00 in an investment earning 12% annually and Tamara places $8,000.00 in an investment every month for 5 years, earning the same percentage.
Who ends up earning more in the future?
Well, well, well, it seems like Marisa's money had quite the growth spurt! Let's calculate the interest rate she got, shall we?
To find the interest rate, we can use the formula for compound interest: A = P(1 + r)^n, where A is the final amount, P is the principal (initial investment), r is the interest rate, and n is the number of years.
In this case, Marisa invested $1650 for 3 years, and her investment grew to $2262.7. So, we have:
2262.7 = 1650(1 + r)^3
Now, let me crunch some numbers for you...
After some mathematical clownery, I've found that the interest rate, compounded annually, is approximately 8.29%. Ta-da!
Please note that this answer is shrouded in whimsy and should not be taken as financial advice. Always consult a professional for serious matters like investments.
To find the interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
In this case, Marisa invests $1650 for 3 years and ends up with $2262.7. So we have:
A = $2262.7
P = $1650
t = 3
Let's assume that the interest is compounded annually, so n = 1.
Now we can rearrange the formula to solve for r:
A = P(1 + r/n)^(nt)
2262.7 = 1650(1 + r/1)^(1*3)
2262.7 = 1650(1 + r)^3
Divide both sides of the equation by 1650:
2262.7/1650 = (1 + r)^3
1.371 = (1 + r)^3
Now take the cube root of both sides:
(1.371)^(1/3) = 1 + r
1.116 = 1 + r
Subtract 1 from both sides:
1.116 - 1 = r
0.116 = r
So the interest rate is approximately 0.116, or 11.6% when rounded to 2 decimal places.
Therefore, an interest rate of 11.6% compounded annually would yield the same results for Marisa's investment.
To find the interest rate, compounded annually, we 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 = interest rate (unknown in this case)
n = number of times interest is compounded per year (since it is compounded annually, n = 1)
t = number of years
We have the following values:
P = $1650
A = $2262.7
n = 1
t = 3 years
Plugging these values into the formula, we get:
2262.7 = 1650(1 + r/1)^(1*3)
Simplifying the equation:
2262.7 = 1650(1 + r)^3
Dividing both sides by the principal amount (1650):
2262.7 / 1650 = (1 + r)^3
Now, we need to find the cube root of both sides to isolate (1 + r):
(2262.7 / 1650)^(1/3) = 1 + r
Subtracting 1 from both sides to solve for r:
(2262.7 / 1650)^(1/3) - 1 = r
Using a calculator, we can calculate (2262.7 / 1650)^(1/3) - 1, which gives us the value of r. Rounding to 2 decimal places, we have:
r = 0.06
Therefore, the interest rate, compounded annually, that would yield the same results is 6%.