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.