How long will it take for R200 000 to grow to R240 000 if the interest rate is 6% per year and interest is compounded every 3 months?
i = .06/4 = .015
n = ?
200000(1.015)^n = 24000
1.015^n = 1.2
take log of both sides
log (1.015^n) = log 1.2
n log 1.015 = log 1.2
n = log 1.2/log 1.015 = 12.25 quarter years
= appr 3 years and 3 weeks
Joseph invests R36000 at a simple rate of 6% per year. How much will thisend amounts to in 6 years and 5 months
To determine how long it will take for an amount to grow from R200,000 to R240,000 with a 6% annual interest rate compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (R240,000)
P = the principal amount (R200,000)
r = annual interest rate (6% or 0.06)
n = number of times interest is compounded per year (4 times, since it's compounded quarterly)
t = time period in years
We need to solve for t, which represents the number of years.
Let's plug in the known values and solve for t:
R240,000 = R200,000(1 + 0.06/4)^(4t)
Dividing both sides of the equation by R200,000:
R240,000/R200,000 = (1 + 0.06/4)^(4t)
1.2 = (1 + 0.015)^(4t)
Taking the natural logarithm (ln) of both sides:
ln(1.2) = ln((1 + 0.015)^(4t))
Using the property of logarithms, ln(a^b) = b * ln(a):
ln(1.2) = 4t * ln(1 + 0.015)
Now we can solve for t by dividing both sides of the equation by 4 times the natural logarithm of (1 + 0.015):
t = ln(1.2) / (4 * ln(1 + 0.015))
Using a calculator, we can find:
t ≈ 4.717 years
Therefore, it will take approximately 4.717 years for R200,000 to grow to R240,000 with a 6% annual interest rate compounded quarterly.