In February of 2018 you entered into a forward rate agreement. According to the forward rate...
In February of 2018 you entered into a forward rate agreement. According to the forward rate agreement, you will borrow $2 million at a continuously-compounded interest rate of 3.45%, with the loan to be taken in February of 2020 and repaid in February of 2023. In February 2019 the continuously-compounded zero rate for a bond maturing in February 2023 is 2.4% and the continuously-compounded forward rate for a loan to be made in February of 2020 and repaid in February 2023 is 3.05%. What is the value to you, in February 2019, of your forward rate agreement? Round all intermediate calculations to six decimal points.
1) -$24,036
2) $37,462
3) -$37,462
4) $0
Homework Answers
As per forward rate contract, the amount to be repaid in Feb, 2023
= P* e^ (rt)
= 2,000,000 * e ^ (0.0345*3) \
= $ 2,218,091.586730
So, interest to be paid = $2218091.586730 - 2000000 = $218091.586730
In Feb, 2019, as the interest rate for the same forward rate has become 3.05%, if the contract had been entered in Feb, 2019 the amount to be repaid in Feb, 2023 would have been
= P* e^ (rt)
= 2,000,000 * e ^ (0.0305*3) \
= $ 2,191,633.553385
So, interest to be paid = $2191633.553385 - 2000000 = $191633.553385
So, The value of the forward rate agreement (FRA) as on Feb,2023 = $191633.553385-$218091.586730 = - $ 26,458.033345
So, the value of FRA in Feb, 2019 = - $26458.033345 * e^ (-0.024 * 4)
= - $24036.171230
The first option is the correct one.
The value of the FRA in Feb, 2023 is -$24036
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