Final answer:
The future value of Heriberto's deposits as of November 26, 2017, is $898,602.89. Heriberto will accumulate $1,500,000 approximately 2.9 years after that date.
Step-by-step explanation:
To calculate the future value of Heriberto's deposits, we can use the compound interest formula: A = P(1 + r/n)^(nt). Where:
A = future value of the investment
P = principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
For the first deposit, P = $100,000, r = 16% = 0.16, n = 4 (compounded quarterly), and t = 3.
So, A = $100,000(1 + 0.16/4)^(4*3) = $100,000(1.04)^(12) = $154,730.46.
For the second deposit, P = $250,000, r = 16% = 0.16, n = 4, and t = 2.5 (since May 26, 2017 to November 26, 2017 is a 2.5-year period).
A = $250,000(1 + 0.16/4)^(4*2.5) = $250,000(1.04)^(10) = $356,451.94.
For the third deposit, P = $300,000, r = 16% = 0.16, n = 4, and t = 1.5 (since May 26, 2017 to November 26, 2017 is a 1.5-year period).
A = $300,000(1 + 0.16/4)^(4*1.5) = $300,000(1.04)^(6) = $387,420.49.
Therefore, the future value as of November 26, 2017, is $154,730.46 + $356,451.94 + $387,420.49 = $898,602.89.
To determine when Heriberto will accumulate $1,500,000, we need to set up an equation:
$898,602.89(1 + 0.16/4)^(4t) = $1,500,000
Solving for t, we find t ≈ 2.9 years.
Therefore, Heriberto will accumulate $1,500,000 approximately 2.9 years after November 26, 2017.
The future value of Heriberto's deposits on November 26, 2017, can be calculated using the compound interest formula for each deposit, with a 16% annual interest rate compounded quarterly. Each deposit's future value is computed separately and then combined to get the total future value. Furthermore, by continuously compounding the total amount, we can determine when it will reach $1,500,000.
To calculate the future value of Heriberto's deposits with an interest rate of 16% per year, compounded quarterly, we use the formula for compound interest. For each deposit, we need to calculate the future value separately and then sum them up.
Calculation for Each Deposit:
First deposit on November 26, 2014: $100,000
Second deposit on May 26, 2015: $250,000
Third deposit on May 26, 2016: $300,000
The quarterly interest rate is 16% per year divided by 4, which is 4% per quarter. We then calculate the total number of quarters for each deposit until November 26, 2017. Finally, using the compound interest formula, FV = P*(1 + r)^n, where FV is the future value, P is the principal amount, r is the quarterly interest rate, and n is the number of quarters, we find the future value for each deposit. Adding these values together gives the total future value as of November 26, 2017.
To determine when Heriberto will have accumulated $1,500,000, we'll continue compounding the total sum calculated until the amount reaches or exceeds $1,500,000.