Question

If an investment is made in a banking entity for an initial amount of 822,000.00 colones in 6 quarters, which obtains an annual return of 11%, but after that period it is decided to carry out a new one investment for 350,000.00 colones additional to the total received from the first investment with a new rate of interest, for 1500 days at a rate of 13%. What amount do you receive at the end of the period in its entirety?

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Answer to a math question If an investment is made in a banking entity for an initial amount of 822,000.00 colones in 6 quarters, which obtains an annual return of 11%, but after that period it is decided to carry out a new one investment for 350,000.00 colones additional to the total received from the first investment with a new rate of interest, for 1500 days at a rate of 13%. What amount do you receive at the end of the period in its entirety?

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Nash

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87 Answers

1. Calculate the future value of the initial investment after 6 quarters with an annual return of 11%:
- The formula for future value is given by

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

- Here,

P = 822,000 \, \text{colones}

r = 0.11

n = 4

(since interest is quarterly), and

t = 1.5

years (since 6 quarters = 1.5 years).
- Substitute the values:

A_1 = 822,000 \left(1 + \frac{0.11}{4}\right)^{4 \times 1.5}

A_1 = 822,000 \left(1 + 0.0275\right)^{6}

A_1 = 822,000 \times 1.171958

A_1 = 963,647.076

2. Calculate the future value of the new investment (initial total from step 1 + additional investment) after 1500 days at a rate of 13%:
- Convert 1500 days to years:

t = \frac{1500}{365}

years.
- Additional investment: 350,000 colones.
- New principal

P_2 = A_1 + 350,000

P_2 = 963,647.076 + 350,000

P_2 = 1,313,647.076

colones.
- Annual interest rate

r = 0.13

.
- Substitute the values in the future value formula:

A_2 = P_2 \left(1 + r\right)^t

A_2 = 1,313,647.076 \left(1 + 0.13\right)^{\frac{1500}{365}}

A_2 = 1,313,647.076 \times 1.529152

A_2 = 2,297,473.701

3. The total amount received at the end of the period is

2,297,473.701

colones.

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