Final answer:
It will take approximately 14.19 years for $75,000 to grow to $100,000 at a simple interest rate of 2.35%, using the formula T = I / (P * R). The given multiple choice options do not include the correct answer.
Step-by-step explanation:
Calculation of Time to Reach a Certain Amount with Simple Interest
To determine how long it will take for $75,000 to grow to $100,000 at a simple interest rate of 2.35%, we need to use the formula for calculating simple interest. The formula is I = PRT, where I is the interest, P is the principal amount (initial amount), R is the annual interest rate in decimal form, and T is the time in years. We need to rearrange the formula to solve for T, which gives us T = I / (P * R).
First, we calculate the total interest needed to reach the target amount:
Interest (I) = Final Amount - Principal AmountInterest = $100,000 - $75,000 = $25,000
Next, we plug the values into the rearranged formula and solve for T:
T = I / (P * R)T = $25,000 / ($75,000 * 0.0235)
By doing the calculations, we find that:
T = $25,000 / $1,762.50 = 14.19
Therefore, it will take approximately 14.19 years for $75,000 to become $100,000 in an account that pays 2.35% simple interest. This means that none of the provided options (a), (b), (c), or (d) are correct.