Sofia and Elena want to save money. They each make a plan to save 2000 pesos a month for the next 10 years. Sofia puts her savings into a clay pot each month. Elaina puts her savings into a bank account paying 2.5% interest. At the end of 10 years how would you expect the totals saved to compare?Group of answer choicesElena's total will likely be more than ten times Sofia's total because of the time of the savings.Sofia's total will likely be much greater than Elena's total because of the safety her savings have.Elena's total will likely be 30000 or more pesos greater than Sofia's total because of the interest her savings accrue.Elena's total will be 2.5% greater than Elena's total because the interestSofia's total and Elena's total are likely similar if not the same.
Question
Sofia and Elena want to save money. They each make a plan to save 2000 pesos a month for the next 10 years. Sofia puts her savings into a clay pot each month. Elaina puts her savings into a bank account paying 2.5% interest. At the end of 10 years how would you expect the totals saved to compare?Group of answer choicesElena's total will likely be more than ten times Sofia's total because of the time of the savings.Sofia's total will likely be much greater than Elena's total because of the safety her savings have.Elena's total will likely be 30000 or more pesos greater than Sofia's total because of the interest her savings accrue.Elena's total will be 2.5% greater than Elena's total because the interestSofia's total and Elena's total are likely similar if not the same.
Solution
Elena's total will likely be 30000 or more pesos greater than Sofia's total because of the interest her savings accrue.
Here's why:
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Sofia saves 2000 pesos a month for 10 years. That's 2000 pesos * 12 months * 10 years = 240,000 pesos.
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Elena does the same, but her money earns 2.5% interest each year. This is a compound interest problem. The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In Elena's case, she's not investing a lump sum, but rather a series of smaller sums (2000 pesos each month). This is known as an annuity. The formula for the future value of an annuity is A = P * [(1 + r/n)^(nt) - 1] / (r/n), where P is the amount deposited each period.
If we plug in the numbers for Elena's situation (P = 2000 pesos/month, r = 2.5% or 0.025 per year, n = 12 times per year, t = 10 years), we find that Elena's savings will amount to approximately 274,070 pesos.
So, Elena's total savings will be significantly more than Sofia's, by approximately 34,070 pesos, thanks to the interest accrued in the bank account.
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