MATH SOLVE

8 months ago

Q:
# 1 A certain company had a document. It gave him the right to receive Q2,000.00 at the end of the years and Q5,000.00 at the end of every three years, during the following 9 years. Each of the payments received was immediately deposited in a bank that received 14% annual interest capitalized semi-annually. How much did you achieve in years?

Accepted Solution

A:

To calculate the amount achieved over the 9 years, we need to find the future value of each payment received at the end of each year and after three years.
Given:
Q2,000.00 received at the end of each year for 9 years.
Q5,000.00 received at the end of every three years for 9 years.
We will calculate the future value of each payment using compound interest with a semi-annual compounding period and a 14% annual interest rate.
First, let's calculate the future value of the annual payments (Q2,000.00) received at the end of each year for 9 years:
FV_annual = P * ((1 + r/n)^(n*t) - 1)
Where:
P = Annual payment amount = Q2,000.00
r = Annual interest rate = 14% = 0.14
n = Number of compounding periods per year (semi-annual compounding) = 2
t = Number of years for each payment = 9
FV_annual = 2000 * ((1 + 0.14/2)^(2*9) - 1)
FV_annual = 2000 * ((1.07)^18 - 1)
FV_annual = 2000 * (4.317575 - 1)
FV_annual = 2000 * 3.317575
FV_annual = Q6,635.15
Next, let's calculate the future value of the payments (Q5,000.00) received at the end of every three years for 9 years:
FV_3years = P * ((1 + r/n)^(n*t) - 1)
Where:
P = Payment amount every three years = Q5,000.00
r = Annual interest rate = 14% = 0.14
n = Number of compounding periods per year (semi-annual compounding) = 2
t = Number of years for each payment (every three years) = 3
FV_3years = 5000 * ((1 + 0.14/2)^(2*3) - 1)
FV_3years = 5000 * ((1.07)^6 - 1)
FV_3years = 5000 * (1.418519 - 1)
FV_3years = 5000 * 0.418519
FV_3years = Q2,092.59
Now, let's calculate the total amount achieved over the 9 years:
Total_Amount_Achieved = (FV_annual * 9) + (FV_3years * 3)
Total_Amount_Achieved = (6635.15 * 9) + (2092.59 * 3)
Total_Amount_Achieved = 59,716.35 + 6,277.77
Total_Amount_Achieved = Q65,994.12
The total amount achieved over the 9 years, taking into account the payments and the interest earned, is Q65,994.12.