What sum of money will accumulate #4800 in 18months if the rate of simple interest is 6%

Answer 1

To find out how much principal P will accumulate to #4800 in 18 months at a simple interest rate of 6%, we use the simple interest formula:

Simple Interest (SI) = P * r * t,

where:
- P is the principal amount (the initial sum of money),
- r is the interest rate per time period, and
- t is the time period in years.

In this case, we know that the final amount A (which includes the principal and the interest) will be #4800, the rate r is 6% or 0.06 when expressed as a decimal, and the time t is 18 months, which is 1.5 years when converted (because there are 12 months in a year).

We also know that the amount A is the sum of the principal P and the simple interest SI:

A = P + SI.

We need to find the initial principal P that will amount to #4800 when interest is applied. The formula for simple interest with respect to the amount A is:

A = P + (P * r * t).

Reordering the formula to solve for P, we get:

P = A / (1 + r * t).

Plugging in the known values:

P = #4800 / (1 + 0.06 * 1.5).

P = #4800 / (1 + 0.09).

P = #4800 / 1.09.

Now we just do the division:

P = #4800 / 1.09,
P = #4403.67 approximately.

So, the principal amount P that will accumulate to #4800 in 18 months with a simple interest rate of 6% is approximately #4403.67.