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you borrow money from a bank at a rate of 7% yearly. you are going to pay the bank $14,869 back after 5 years and $10,161 back after 10 years. how much will the bank give you today?

User SPMP
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1 Answer

5 votes

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.

User Jianpx
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