A debt can be repaid by payments of $4000 today, $4000 in five years, and $3000...
A debt can be repaid by payments of $4000 today, $4000 in five years, and $3000 in six years. What single payment would settle the debt one year from now if money is worth 7% compounded semi annually?
Homework Answers
Interest rate is compounded semiannually. So,
Effective annual rate = [( 1 + 7% / 2) ^ 2] - 1
= 1.071225 - 1
= 7.1225%
Effective annual rate is 7.1225%.
Present value of total Payment = $4,000 + [$4,000 / (1 + 7.1225%) ^ 5] + [$4,000 / (1 + 7.1225%) ^ 6]
= $4,000 + $2,835.8 + $247.
= $9,482.81.
Present value of total Payment is $9,482.81.
One time payment after one year = $9,482.81 × (1 + 7.1225%)
= $10,158.22.
One time payment after 1 year is $10,158.22.
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