The following recurrence relation can be used to model a compound interestinvestment of $45 000 paying interest compounding at the rate of 7.5% per year.𝑉0 = 45 000, 𝑉𝑛+1 = 1.075𝑉𝑛Use the recurrence relation to find the value of the investment after 12 years

To find the value of the investment after 12 years, we need to apply the recurrence relation for 12 times.

The recurrence relation is given by 𝑉𝑛+1 = 1.075𝑉𝑛. This means that to get the value of the investment at year n+1, we multiply the value of the investment at year n by 1.075.

We start with 𝑉0 = 45 000.

Now we apply the recurrence relation:

Year 1: 𝑉1 = 1.075 * 45 000 Year 2: 𝑉2 = 1.075 * 𝑉1 Year 3: 𝑉3 = 1.075 * 𝑉2 ... Year 12: 𝑉12 = 1.075 * 𝑉11

We can simplify this process by realizing that the value of the investment after n years is just the initial investment multiplied by 1.075^n.

So, the value of the investment after 12 years is 𝑉12 = 45 000 * (1.075)^12.

Now you just need to calculate this expression to get the final result.

To find the value of the investment after 12 years using the given recurrence relation, we follow these steps:

1. Identify the initial value and the rate of interest. In this case, the initial value V0 is $45,000 and the interest rate is 7.5% per year, which is represented as 1.075 in the recurrence relation.

2. Understand the recurrence relation. The relation Vn+1 = 1.075Vn means that each year's value is 1.075 times the previous year's value.

3. Apply the recurrence relation for 12 years. This means we multiply the initial value by 1.075 twelve times.

Mathematically, this can be represented as:

V12 = V0 * (1.075)^12

4. Substitute the given values into the equation:

V12 = 45000 * (1.075)^12

5. Calculate the result.

After performing the calculation, you will get the value of the investment after 12 years.

To find the value of the investment after 12 years, we need to apply the recurrence relation for 12 times.

The recurrence relation is given by 𝑉𝑛+1 = 1.075𝑉𝑛. This means that to get the value of the investment in the next year, we multiply the value of the investment in the current year by 1.075.

We start with 𝑉0 = 45 000.

Now we apply the recurrence relation:

Year 1: 𝑉1 = 1.075 * 45 000 Year 2: 𝑉2 = 1.075 * 𝑉1 Year 3: 𝑉3 = 1.075 * 𝑉2 ... Year 12: 𝑉12 = 1.075 * 𝑉11

We can simplify this process by realizing that the value of the investment after n years is just the initial investment multiplied by 1.075^n.

So, the value of the investment after 12 years is 𝑉12 = 45 000 * (1.075)^12.

Now, you just need to calculate this expression to get the final answer.