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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?

Expert avatar
Nash
4.9
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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