Question

Determine the number of compounding periods for the following investment

Principal: $1832
Future value $2193
Interest rate 8.1%
Frequency of conversion monthly

Answer 1

To find the number of compounding periods, we can use the formula:

n = (t x f)

where:

n = number of compounding periods

t = time in years

f = frequency of conversion

We are given that the principal is $1832, the future value is $2193, the interest rate is 8.1%, and the frequency of conversion is monthly. We need to find the time in years.

To find the time in years, we can use the formula:

FV = PV x (1 + r/n)^(nt)

where:

FV = future value

PV = present value

r = interest rate

n = number of compounding periods per year

t = time in years

Substituting the given values, we get:

$2193 = $1832 x (1 + 0.081/12)^(12t)

Simplifying this equation, we get:

1.1971^(12t) = 1.1971

Taking the natural logarithm of both sides, we get:

12t x ln(1.1971) = ln(1.1971)

Solving for t, we get:

t = ln(1.1971) / (12 x ln(1.1971))

t = 3 years

Now that we know the time in years, we can find the number of compounding periods:

n = (t x f)

n = (3 x 12)

n = 36

Therefore, the number of compounding periods is 36.

Answer 2

Answer: There is 1 compounding period for this investment.

Step-by-step explanation: To determine the number of compounding periods, we can use the following formula:

n = (t / p) * m

where:

n = number of compounding periods

t = time period in years

p = payment frequency per year

m = compounding frequency per payment period

In this case, we have:

Principal = $1832

Future value = $2193

Interest rate = 8.1%

Payment frequency = 12 (monthly)

First, let's calculate the time period in years:

t = 1 year / 12 months = 0.0833 years

Next, let's determine the compounding frequency per payment period:

m = 12 (since interest is compounded monthly)

Now we can calculate the number of compounding periods:

n = (t / p) * m = (0.0833 / 1) * 12 = 1

Therefore, there is 1 compounding period for this investment.