Final answer:
The present value of the future payments can be calculated using the formula for present value of an annuity. The bank would give you $11,065.64 today if you pay back after 5 years, and $5,619.98 today if you pay back after 10 years.
Step-by-step explanation:
To find the amount that the bank would give you today, we need to calculate the present value of the future payments using the formula for present value of an annuity:
Present Value = Future Value / (1 + r)^n
where Future Value is the sum of all the payments, r is the interest rate, and n is the number of years.
Using the given information, the Future Value is $14,869 after 5 years and $10,161 after 10 years. The interest rate is 7% or 0.07, and the number of years is 5 and 10, respectively.
Substituting the values into the formula:
Present Value after 5 years = $14,869 / (1 + 0.07)^5 = $11,065.64
Present Value after 10 years = $10,161 / (1 + 0.07)^10 = $5,619.98
Therefore, the bank would give you $11,065.64 today if you pay back after 5 years, and $5,619.98 today if you pay back after 10 years.