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#mathematics
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#finance
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An investment of R7000 accumulates R8261in a certain interval of time at the rate of 4% per annum if compound interest. Find the time?
To find the time it takes for an investment to accumulate to R8261 at a rate of 4% per annum with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where: A = the amount accumulated (R8261) P = the principal amount (R7000) r = the annual interest rate (4% or 0.04) n = the number of times interest is compounded per year (assuming it is compounded annually, n = 1) t = the time the money is invested for (in years)
Plugging in the values we have:
8261 = 7000(1 + 0.04/1)^(1*t)
8261 = 7000(1.04)^t
8261/7000 = 1.04^t
1.18014 = 1.04^t
Taking the natural logarithm of both sides:
ln(1.18014) = ln(1.04^t)
ln(1.18014) = t*ln(1.04)
t = ln(1.18014) / ln(1.04)
t ≈ 3 years
Therefore, it will take approximately 3 years for an investment of R7000 to accumulate to R8261 at a rate of 4% per annum with compound interest.