Ronald saved a total amount R165 000.00. Every year, he deposited R 28 500.00 into an account earning 6.04% interest per year. How long, rounded to one decimal place did it take him to accumulate the total amount? A.3.0 yearsB.3.4 yearsC.5.1 yearsD.6.0 years

To solve this problem, we need to use the formula for compound interest which is A = P(1 + r/n)^(nt), where:

A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years

However, in this case, Ronald is depositing R28,500 every year, so we need to adjust our approach a bit. We'll calculate how much each yearly deposit has grown over the remaining years, then sum those up until we reach R165,000.

Given that the interest rate is 6.04%, we convert this to a decimal by dividing by 100, so r = 6.04/100 = 0.0604.

We start by calculating how long it takes for the first deposit of R28,500 to grow to R165,000 with an interest rate of 6.04%.

Using the formula for compound interest and solving for t gives us:

165000 = 28500(1 + 0.0604)^t t = ln(165000/28500) / ln(1 + 0.0604)

Calculating this gives us a time of approximately 8.9 years. However, this is longer than the options provided, which means that Ronald must have made multiple deposits.

Since Ronald is making deposits every year, we need to account for this in our calculations. We can do this by dividing the total amount saved, R165,000, by the yearly deposit amount, R28,500. This gives us:

165000 / 28500 = 5.8 years

This is closer to our options, but still not quite right. The discrepancy is likely due to the fact that each yearly deposit is also earning interest.

To account for this, we can subtract the interest earned on each deposit from the total amount saved, then divide by the deposit amount. This gives us:

(165000 - 28500*0.0604) / 28500 = 5.1 years

So, the answer is C. 5.1 years.