Final answer:
Juan faces two investment strategies for his kids' education with both involving compound interest calculations. Strategy A focuses on earlier investment, growing for a longer period, often resulting in more savings. Strategy B starts later with more contributions but has less time to benefit from compound interest.
Step-by-step explanation:
Juan is considering two different strategies for investing money in his children's education, both involving compound interest. Juan invests $50 per month for 5 years at an annual rate of 8% compounded monthly. After the investment period, the amount will continue to grow for another 13 years without additional contributions. To calculate the future value of such an annuity, we'd use the future value of a series formula:
where P is the monthly payment, r is the monthly interest rate, and n is the number of months.
The first calculation for the 5 years will get us the accumulated value after the contribution period. We'll then use the future value of a single sum to grow the amount equivalent to the end of the 5 years by a further 13 years.
Juan delays his investment for 5 years but then deposits $50 a month for the next 13 years into the same type of account. Here we'll only use the future value of a series formula, as there is no period of growth without contributions after the 13 years. After performing the calculations, we can compare the final amount from both scenarios to determine which strategy is more effective for Juan's goals.