Adam and Enzo want to save money. They each make a plan to save 200 Euro a month for the next 10 years. Adam puts his savings into a box each month. Enzo puts his 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 choicesAdam's total will likely be much greater than Enzo's total because of the safety his savings have.Adam's total and Enzo's total are likely similar if not the same.Enzo's total will be 2.5% greater than Adam's total because the interestEnzo's total will likely be more than ten times Adam's total because of the time of the savings.Enzo's total will likely be 3000 or more Euro greater than Adam's total because of the interest his savings accru
Question
Adam and Enzo want to save money. They each make a plan to save 200 Euro a month for the next 10 years. Adam puts his savings into a box each month. Enzo puts his 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 choicesAdam's total will likely be much greater than Enzo's total because of the safety his savings have.Adam's total and Enzo's total are likely similar if not the same.Enzo's total will be 2.5% greater than Adam's total because the interestEnzo's total will likely be more than ten times Adam's total because of the time of the savings.Enzo's total will likely be 3000 or more Euro greater than Adam's total because of the interest his savings accru
Solution
Enzo's total will likely be 3000 or more Euro greater than Adam's total because of the interest his savings accrue.
Here's why:
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Adam saves 200 Euro a month for 10 years, which is 120 months. So, Adam's total savings will be 200 Euro * 120 months = 24,000 Euro.
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Enzo also saves 200 Euro a month, but his savings earn an interest of 2.5% per annum. This is a case of compound interest, where the interest is added to the principal amount and the next interest is calculated on the new total.
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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.
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In Enzo's case, he's not investing a lump sum amount, but a certain amount every month. So, we need to use the formula for the future value of a series of payments (or an annuity), which is: A = P * [(1 + r/n)^(nt) - 1] / (r/n)
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Substituting the given values into the formula, we get: A = 200 * [(1 + 0.025/12)^(12*10) - 1] / (0.025/12)
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Calculating the above expression will give us the total amount saved by Enzo at the end of 10 years.
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Comparing the totals saved by Adam and Enzo, we can see that Enzo's total will be significantly greater than Adam's total due to the interest accrued on his savings.
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