Interest rate problems Answer both a, b, and c a. Mary makes Susan a $1.000 loan

Question

Interest rate problems Answer both a, b, and c a. Mary makes Susan a $1.000 loan. Susan agrees to pay Mary $1,210 at the ened of 2 years. Calculate Mary's yield to maturity on this loan. b. One year after the loan is made Mary needs money. Rachel agrees to pay Mary $1,050 for the loan to Susan. (Susan will now pay Rachel the $1,210 at the end of the second year.) Calculate Mary's rate of return for the one year she held the loan. Calculate Rachel's yield to maturity for the remaining one year of the loan. What does this imply about how interest rates changed between the time Mary made the loan and the time she sold it to Rachel? c. You put $1,000 into a savings account on which you earn 10% per year. You do not make any withdrawals. How much do you have at the end of 2 years?

Explanation / Answer

a. PV = 1000, FV = 1210, n=2, r = ?

FV = PV * (1+r)^n; 1210 = 1000 * (1+r)^2

Solving, we get r (Yield to maturity) = 10%

b. Amount at the end of year 1 = 1050; Current amount = 1000

Rate of return at the end of year 1 to Mary = (Amount at the end of year 1 - Current amount)/Current amount = (1050 - 1000)/1000 = 50/1000 = 5%

PV = 1050, FV = 1210, n=1, r = ?

FV = PV * (1+r)^n; 1210 = 1050 * (1+r)^1

Solving, we get r for Rachel (Yield to maturity) = (1210/1050) - 1 = 15.24%

c. PV = 1000, r = 10%, n=2, FV = ?

FV = PV * (1+r)^n = 1000 * (1+10%)^2

Solving, we get FV = 1210

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