Question

Compound interest formula: v (t) = p (1 startfraction r over n endfraction) superscript n t. How long does it take to double a $1,000 investment that pays 6.5% annual interest, compounded monthly? Which equation can you use to solve this problem?

1) 1000 = (1 startfraction 0.065 over 12 endfraction) superscript t
2) 2 = (1 startfraction 0.065 over 12 endfraction) superscript 12 t
3) 1000 = (1 startfraction 0.065 over 12 endfraction) superscript 12 t
4) 2 = (1 startfraction 0.065 over 12 endfraction) superscript t

Answer 1

To determine how long it takes for a $1,000 investment to double with 6.5% interest compounded monthly, use the compound interest formula and set 2 equal to (1 + 0.065/12)12t. The correct equation to use is the second option provided.

Step-by-step explanation:

To find out how long it takes to double a $1,000 investment with a 6.5% annual interest rate compounded monthly, we'll use the compound interest formula: v(t) = p (1 + r/n)nt, where:

• p is the principal amount ($1,000)
• r is the annual interest rate (6.5%, or 0.065 as a decimal)
• n is the number of times interest is compounded per year (12)
• t is the number of years

We want the future value v(t) to be double the principal, so we set v(t) = 2p. Therefore, our equation to solve is:

2 = (1 + 0.065/12)12t

The correct equation from the provided options is the second one: 2 = (1 + 0.065/12)12t. This equation represents the relationship between the variables to determine the time t to double the investment.