At what rate must $500 be compounded for it to grow to 1079.46 in 10 years?
8 percent? i think
correct.
500*(1+r)^10 = 1079.46 -- solve for r.
To calculate the rate at which $500 must be compounded in order to grow to $1079.46 in 10 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount ($1079.46)
P = Initial principal ($500)
r = Annual interest rate (unknown)
n = Number of times interest is compounded per year (unknown)
t = Number of years (10)
To find the rate, we need to solve for r. Let's substitute the given values into the formula:
1079.46 = 500(1 + r/n)^(nt)
Now, since both r and n are unknown, we cannot directly solve for the rate. However, if we assume that the interest is compounded annually (n = 1), we can solve for r.
1079.46 = 500(1 + r/1)^(1*10)
1079.46 = 500(1 + r)^10
Dividing both sides by 500:
2.15892 = (1 + r)^10
Taking the 10th root of both sides:
(1 + r) = 2.15892^(1/10)
(1 + r) = 1.08
Subtracting 1 from both sides:
r = 0.08
Therefore, the annual interest rate required for $500 to grow to $1079.46 in 10 years is 8%.
To calculate the rate at which $500 must be compounded, we need to use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A is the final amount ($1079.46 in this case)
P is the principal amount ($500 in this case)
r is the annual interest rate (what we need to find)
n is the number of times interest is compounded per year (unknown)
t is the time in years (10 years in this case)
First, we need to rearrange the formula to solve for r:
r = ((A / P)^(1/(n*t))) - 1
Now we can substitute the given values:
r = ((1079.46 / 500)^(1/(n*10))) - 1
To find the interest rate, let's try assuming a compounding period of annually (n = 1):
r = ((1079.46 / 500)^(1/(1*10))) - 1
r = (2.15892)^(1/10) - 1
r = 1.08074 - 1
r = 0.08074
So, the annual interest rate required for $500 to grow to $1079.46 in 10 years, when compounded annually, is approximately 8.07%.