Question

Laurent invested some money in a bank account. The relationship between the elapsed time, tt, in decades, since Laurent invested the money, and the total amount of money in the account, mdecade(t)mdecade​(t), in dollars, is modeled by the following function:mdecade(t)=P×(1+r)tmdecade​(t)=P×(1+r)tWhere PP is the principal amount, rr is the interest rate, and tt is the time in decades. If Laurent invested $5,000 at an interest rate of 4% per decade, what will be the total amount in the account after 3 decades?

a) $6,565.60
b) $7,040.00
c) $7,424.00
d) $8,157.60

Answer 1

Using the compound interest formula, the total amount in the bank account after 3 decades with a principal of $5,000 and an interest rate of 4% per decade is $5,624.32. The correct answer is not listed in the provided options.

Step-by-step explanation:

The student has asked about the total amount of money in a bank account after 3 decades given an initial investment using compound interest. With a principal amount of $5,000, an interest rate of 4% per decade, and a time period of 3 decades, we can use the compound interest formula:

decade(t) = P × (1 + r)^t

Plugging in the values:

mdecade(3) = $5,000 × (1 + 0.04)^3

mdecade(3) = $5,000 × (1.04)^3

mdecade(3) = $5,000 × 1.124864

mdecade(3) = $5,624.32

Therefore, the total amount in the account after 3 decades would be $5,624.32, which means the correct answer is not listed among the options provided by the student.