Question

If $2500 is invested at an interest rate of 3.5% per year, compounded daily, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)

A) $2671.88

B) $2779.14

C) $2888.29

D) $2999.15

Answer 1

To find the value of the investment after a given number of years with compound interest, we can use the formula: A = P(1 + r/n)^(nt). In this case, P = $2500, r = 3.5% (or 0.035 as a decimal), n = 365 (since interest is compounded daily), and t is the number of years given. Based on the options given, the value of the investment after the given number of years is approximately $2,779.14 (Option B).

Step-by-step explanation:

To find the value of the investment after a given number of years with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

• A = the future value of the investment
• P = the principal amount (initial investment)
• r = the annual interest rate (as a decimal)
• n = the number of times interest is compounded per year
• t = the number of years

In this case, P = $2500, r = 3.5% (or 0.035 as a decimal), n = 365 (since interest is compounded daily), and t is the number of years given.

Plugging in the values, we can calculate the future value of the investment:

A = 2500(1 + 0.035/365)^(365t)

Since the answer options are rounded to the nearest cent, we need to solve for t by trying each option until we find the closest answer. Based on the options given, the value of the investment after the given number of years is approximately $2,779.14 (Option B).