Imagine you are taking out a 10,000 USD loan, at a rate of 10.3% per year. In ex

Question

Imagine you are taking out a 10,000 USD loan, at a rate of 10.3% per year. In exchange, you promise to make 5 equal annual payments at the end of each year for the next five years. What must be the amount of each of your payments in order to satisfy the lender? You must set the payment to such an amount that the sum of the present values of all of them add up to 10,000 USD, so that the lender is willing to give you that money in exchange for your future promised payments. Recall the present value of annuity formula we derived in class - it might be helpful here.

Explanation / Answer

1)

interest rate after inflation = 3.22 - 0.62 = 2.6%

amount after 1 year = 1000 * (1+0.026) = 1026

interest payment = 26

2) interest earned = 57

expected return = 57/943 = 6.05%

3)
coupon payment = 44

price = 44 * PVIFA(5.1%,3) + 1000 * PVIF(5.1%,3)

= 44 * 2.7182 + 1000 * 0.8614

= 981

4)

let x be the equal payments

PV = 10000

x * [1 - (1+0.103)^-5]/0.103 = 10000

x = 2658.22 ..........ans

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