The Fresh and Green Company has a savings plan for employees. If an employee makes an initial deposit of $1000, the company pays 8% interest compounded quarterly. How many years will the employee need to leave the money in the account to have $5000?
19 years
20 years
21 years
22 years
again, the formula...
1000(1+.08/4)^(4t)=5000
Now just solve for t.
P = Po(1+r)^n = 5000,
Po = $5000.
r = 0.08/4 = 0.02.
n = The number of compounding periods.
1000(1.02)^n = 5000,
(1.02)^n = 5,
n*Log1.02 = Log5,
n = 81.274 Compounding periods.
T = 81.274Comp. * 1yr./4Comp. = 20.32 Yrs.
post
To find out how many years the employee needs to leave the money in the account to have $5000, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment ($5000 in this case)
P = the principal amount (initial deposit of $1000)
r = annual interest rate (8% or 0.08 as a decimal)
n = number of times interest is compounded per year (quarterly, which is 4 times)
t = number of years
We want to solve for t, so let's rewrite the formula to isolate t:
A/P = (1 + r/n)^(nt)
Substituting the given values:
5000/1000 = (1 + 0.08/4)^(4t)
Simplifying further:
5 = (1 + 0.02)^(4t)
Taking the natural logarithm of both sides to remove the exponent:
ln(5) = ln([(1 + 0.02)^(4t)])
Using properties of logarithms, we can bring down the exponent:
ln(5) = 4t ln(1.02)
Finally, dividing both sides by 4 ln(1.02) to solve for t:
t = ln(5) / (4 ln(1.02))
Using a calculator, we find that t is approximately 19.69. Since t represents the number of years, we round it up to the nearest whole number.
Therefore, the employee will need to leave the money in the account for approximately 20 years to have $5000.