Final answer:
After 3 years, using a 3% annual interest rate compounded annually on a principal amount of $30,000, the total amount would be approximately $32,781.81. However, using simple interest, the answer would be $32,700, which is not listed among the multiple-choice options, suggesting there might be a typo in the question.
Step-by-step explanation:
Your grandmother is an example of how starting to save money early and benefiting from compound interest can be beneficial. In this situation, she has placed $30,000 in an account with a 3% annual interest rate. The question is: How much is in the account after 3 years? Let's calculate this using the formula for compound interest, which is A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time in years.
Since the interest is compounded annually, n will be 1. Thus, the formula simplifies to A = P(1 + r)t. Plugging in the numbers:
A = $30,000(1 + 0.03)3
A = $30,000(1.03)3
A = $30,000(1.092727)
A = $32,781.81 approximately.
However, since this exact number is not one of the options provided, it appears that we are meant to use simple interest rather than compound interest for the calculation. The simple interest formula is I = P * r * t, where I is the interest, P is the principal amount, r is the annual interest rate (in decimal form), and t is the time in years. Thus:
I = $30,000 * 0.03 * 3
I = $2,700
This means the total amount in the account after 3 years using simple interest would be:
Total = P + I
Total = $30,000 + $2,700
Total = $32,700
Therefore, the closest answer to our calculations is $32,700, which suggests a typo in the multiple-choice options provided in the question.