An investor has $5,000 on 3/30 for 90 days and decides to place it for a fixed term that is renewed every 30 days, at a nominal annual rate of 72%. The following is requested: a.- What will be the amount of the certificate at maturity? b.- How much is the total interest on the operation?

To solve this problem, we need to calculate the amount of the certificate at maturity and the total interest on the operation.

a. To calculate the amount of the certificate at maturity, we use the formula for compound interest:

$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$

Where:
A = the final amount
P = the initial principal (initial investment)
r = the nominal annual rate (as a decimal)
n = the number of times that interest is compounded per year
t = the time in years

Given:
P = $5,000
r = 72% = 0.72 (as a decimal)
n = 360/30 = 12 (since the interest is compounded every 30 days)
t = 90/360 = 0.25 years (since 90 days is 0.25 years)

Substituting the values into the formula:

$$A = 5000 \left(1 + \frac{0.72}{12}\right)^{(12 \cdot 0.25)}$$

Simplifying:

$$A = 5000 \left(1 + 0.06\right)^3$$

$$A = 5000 \cdot 1.191016$$

$$A = $5,955.08$$

Therefore, the amount of the certificate at maturity will be $5,955.08.

b. To calculate the total interest on the operation, we subtract the initial investment from the final amount:

$$Total\ Interest = A - P$$

$$Total\ Interest = $5,955.08 - $5,000$$

$$Total\ Interest = $955.08$$

Therefore, the total interest on the operation will be $955.08.

Answer:
a. The amount of the certificate at maturity will be $5,955.08.
b. The total interest on the operation is $955.08.