Sindi saved a total amount of R 105000.Every year, she deposited 28500.00 into an account earning 6.04% interest per year. How long, roudended to one decimal place did it take him the total amount?

To find out how long it took Sindi to save a total of R 105000, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = Total amount saved (R 105000)
P = Initial deposit (R 28500)
r = Annual interest rate (6.04% or 0.0604)
n = Number of times interest is compounded per year (assuming once per year)
t = Number of years

Plugging in the values we have:

105000 = 28500(1 + 0.0604/1)^(1*t)

105000 = 28500(1.0604)^t

105000/28500 = (1.0604)^t

3.684210526 = (1.0604)^t

Taking the natural logarithm of both sides to solve for t:

ln(3.684210526) = ln((1.0604)^t)

ln(3.684210526) = t*ln(1.0604)

t = ln(3.684210526)/ln(1.0604)

t ≈ 5.0 years

Therefore, it took Sindi approximately 5.0 years to save a total of R 105000.

Step 1: Calculate the annual interest earned

Interest earned in one year = R 105000 - 6.04% = R 6381.00

Step 2: Calculate the annual amount saved by Sindi

Annual amount saved = R 28500.00

Step 3: Determine how many years it takes to reach R 105000

Number of years = R 105000 / R (annual amount saved + annual interest)

Substituting the values we calculated:

Number of years = R 105000 / R (28500.00 + 6381.00)
= R 105000 / R 34881.00
= 3.01 years

Therefore, it took Sindi approximately 3.0 years to save R 105000.