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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?

Apr 13

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Apr 13

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.

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.