Question

What is the formula for compound interest?

a) A = P(1 + r/n)^nt
b) A = P(1 + r)^n
c) A = P + rt
d) A = Pr/n

In the formula A = P(1 + r/n)^nt, what does 'n' represent?
a) Number of years
b) Number of × interest is compounded per year
c) Principal amount
d) Interest rate

If $1500 is invested at 6% interest compounded monthly, how long does it take to double?
a) 10 years
b) 12 years
c) 8 years
d) 6 years

Answer 1

The formula for compound interest is A = P(1 + r/n)^nt. In this formula, 'n' represents the number of times the interest is compounded per year. To calculate how long it takes to double an investment with $1500 at 6% interest compounded monthly, use the compound interest formula and solve for 't', which is approximately 11.55 years.

Step-by-step explanation:

The formula for compound interest is A = P(1 + r/n)^nt. In this formula, 'n' represents the number of times the interest is compounded per year.

If $1500 is invested at 6% interest compounded monthly, to calculate how long it takes to double the investment, we need to use the formula. Let's solve it step-by-step:

1. Principal (P) = $1500
2. Interest rate (r) = 6% = 0.06
3. Number of times interest is compounded per year (n) = 12 (monthly)
4. Time (t) = unknown
5. Future value (A) = 2 x P = 2 x $1500 = $3000

Now, plug in the given values into the compound interest formula:

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

$3000 = $1500(1 + 0.06/12)^(12t)

Next, we can simplify the formula:

2 = (1.005)^12t

To solve for 't', we can take the natural logarithm (ln) of both sides:

ln(2) = ln((1.005)^12t)

ln(2) = 12t ln(1.005)

Divide both sides by 12 ln(1.005):

t = ln(2) / (12 ln(1.005))

Using a calculator, we can find that 't' is approximately 11.55 years.