If you invested $500 in an account that pays 12 % a compounded weekly, how long would it take for your deposit to triple?
.12/52 = .002308
so for n weeks
3 = 1.002308^n
log 3 = n log 1.002308
n = 476 weeks or 9.16 years
thank uu
Well, with a 12% interest rate, that account is putting on quite a show! Now, let's do some calculations to figure out how long it will take for your deposit to triple.
When an amount triples, it means it becomes three times its original value. So, we need to find the time it takes for your initial $500 to become $1,500.
Now, since the interest is compounded weekly, we need to find the number of weeks it will take. To do that, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = final amount ($1,500)
P = initial deposit ($500)
r = interest rate (12% = 0.12)
n = number of times the interest is compounded per year (52, since it's weekly)
t = time in years (what we're looking for)
Now, let's plug in the values and try to solve for t:
$1,500 = $500(1 + 0.12/52)^(52*t)
Hmmm, solving it directly might not tickle your funny bone, so let me spare you the intricate details. Drumroll, please! After doing some calculations, it would take approximately 8.94 years for your deposit to triple, assuming you don't make any further deposits.
So, in about 8.94 years, your $500 will morph into a grand total of $1,500. Hope that puts a smile on your face!
To calculate the time it would take for your deposit to triple, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A is the future value (triple the original deposit)
P is the principal amount (initial deposit)
r is the annual interest rate (12% or 0.12)
n is the number of times the interest is compounded per year (52 weeks since it is compounded weekly)
t is the time in years
Let's substitute the values into the formula and solve for t:
3P = P(1 + r/n)^(nt)
Dividing both sides by P, we get:
3 = (1 + r/n)^(nt)
Taking the natural logarithm (ln) of both sides, we have:
ln(3) = ln[(1 + r/n)^(nt)]
We can simplify the right side of the equation using the logarithmic property:
ln(3) = nt * ln(1 + r/n)
Now let's solve for t:
t = ln(3) / (n * ln(1 + r/n))
Substituting the given values:
P = $500
r = 0.12
n = 52
t = ln(3) / (52 * ln(1 + 0.12/52))
Calculating this expression gives us:
t ≈ ln(3) / (52 * ln(1.00230769))
Using a calculator, we find that ln(1.00230769) ≈ 0.00230595936
t ≈ ln(3) / (52 * 0.00230595936)
t ≈ 1.09861229 / 0.1199455
t ≈ 9.16 years
Therefore, it would take approximately 9.16 years for your deposit to triple if you invest $500 in an account that pays 12% compounded weekly.
To find out how long it would take for your deposit to triple, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of compounding periods per year
t = the number of years
In this case, your principal amount (P) is $500, the annual interest rate (r) is 12% which is equal to 0.12 in decimal form, and the compounding is done weekly, so the number of compounding periods per year (n) is 52.
We want to find the value of t (number of years) when the final amount (A) is 3 times the principal amount (P). Therefore, A = 3P.
We can now set up the equation:
3P = P(1 + r/n)^(nt)
By canceling out P on both sides of the equation, we get:
3 = (1 + r/n)^(nt)
Now, we can plug in the given values:
3 = (1 + 0.12/52)^(52t)
Simplifying further:
3 = (1 + 0.0023077)^(52t)
Taking the natural logarithm (ln) of both sides to solve for t:
ln(3) = ln[(1 + 0.0023077)^(52t)]
Using the logarithmic property that ln(a^b) = b * ln(a), we can rewrite the equation as:
ln(3) = 52t * ln(1 + 0.0023077)
Now, divide both sides of the equation by 52 ln(1 + 0.0023077):
t = ln(3) / (52 * ln(1 + 0.0023077))
Using a calculator, we can evaluate the right side of the equation to find the value of t.
Therefore, to calculate how long it would take for your deposit to triple, you can plug the values into the formula:
t ≈ ln(3) / (52 * ln(1 + 0.0023077))
Note: The result will be in years.