Question

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

Answer 1

[AI-generated answer — Bot GPT-4 Turbo]

To calculate the sum of money that will accumulate to $4800 in 18 months at a simple interest rate of 6%, we need to understand the formula for simple interest:

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

In this case:
Simple Interest (SI) = The total interest earned at the end of 18 months
Principal (P) = The initial sum of money we're trying to calculate
Rate (R) = The annual interest rate (6% or 0.06 as a decimal)
Time (T) = The time period the money is invested or borrowed for, in years

Since we want to know the Principal (P), we need to rearrange the formula to solve for P.

First, let's find out the interest earned (SI) by subtracting the Principal from the final amount ($4800). However, in this problem, we do not know the Principal, only the final amount including interest. Therefore, we need to alter our approach to:

P + SI = Total Amount
P + (P × R × T) = Total Amount

P × (1 + R × T) = Total Amount

Convert the interest rate R to a decimal and the time T to years. For 18 months, the time in years is:

T = 18 months ÷ 12 months/year = 1.5 years

Now we can substitute R and T into the equation:

P × (1 + 0.06 × 1.5) = $4800

Calculate the term in the parentheses:

P × (1 + 0.09) = $4800
P × 1.09 = $4800

Now, solve for P:

P = $4800 ÷ 1.09
P ≈ $4403.67

Therefore, the sum of money that will accumulate to $4800 in 18 months with a simple interest rate of 6% is approximately $4403.67.