Task $2$: Adjustable$-$Rate Mortgages

$$ Loan amount $$145,000,000$

$$ Initial rate $5\mathrm{.}75\%$

$$ Index $1-$year Treasury Bill

$$ Adjustment interval $1$ year

$$ Margin $2\mathrm{.}5\%$

$$ Floor$/$cap $2\mathrm{.}5\%$ annual, $5\%$ lifetime based on initial index plus margin

$$ Payment interval annual

$$ Term $10$ years

$$ Fully amortizing over $25$ years

$$ Payments made quarterly

$2\%$ origination fee, $3\%$ prepayment penalty

Exhibit $1$ below shows the data you have obtained from the yield curve published by the Department of the

Treasury.

$1.$ Find the expected interest rate schedule for the first five years.

$2.$ Find the effective annual rates for the loan considered for the first five years.

$3.$ Find the expected payment schedule for the first five years.

Exhibit $1$: Yield Curve

Time to Maturity Yield to Maturity

$15\mathrm{.}10\%$

$25\mathrm{.}65\%$

$35\mathrm{.}94\%$

$46\mathrm{.}13\%$

$56\mathrm{.}15\%$

$66\mathrm{.}19\%$

$76\mathrm{.}24\%$

$86\mathrm{.}31\%$

$96\mathrm{.}43\%$

$106\mathrm{.}71\%$