Help me Bobpursley is dumb
Serge invests $700 at 5.75% per year,
compounded quarterly. When the account
is closed, its value will be $950. How long
will Serge’s money be invested?
See the prior post, I found the error.
To find out how long Serge's money will be invested, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (in this case, $950)
P = the principal amount (in this case, $700)
r = the annual interest rate (in decimal form, so 5.75% = 0.0575)
n = the number of times interest is compounded per year (in this case, quarterly, so n = 4)
t = the number of years
Now, let's plug in the given values and solve for t:
950 = 700(1 + 0.0575/4)^(4t)
First, divide both sides of the equation by 700:
1.357142857 = (1 + 0.0575/4)^(4t)
Next, subtract 1 from both sides:
0.357142857 = (0.0575/4)^(4t)
To isolate the exponent term, we take the logarithm (base 0.357142857) of both sides:
log(0.357142857)(0.357142857) = log(0.0575/4)^(4t)
Simplifying the left side:
1 = 4t * log(0.0575/4)
Divide both sides by 4 * log(0.0575/4):
t = 1 / (4 * log(0.0575/4))
Using a calculator, we can find the value of t to be approximately 4.83 years. Therefore, Serge's money will be invested for around 4.83 years.