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bonds- formula to calculate amount of principal in a loan

Sold at discount
P<C
Discount =C-P
Sold at premium
P>C
Premium = P-C
How to calculate book value for bonds
PRICE IS PRESENT VALUE OF FUTURE CASH FLOWS

Callable bonds what price is the most advantageous to assume a yield %
The lowest price because it is out worst case scenario
If there is no call premium what time does the smallest yield occurs where
If bought at premium- earliest callable date
If bought at discount - latest callable date
Forward rate formula

When accumulating with spot rates what interest rate do you use
The one in the last period (or period you are accumulating to)
How to calculate surplus
Assets - liabilities
Absolute/ exact matching

MacD definition

MacD how to calculate

Modified duration

Zero coupon bond what does MacD and ModD ewual
Years to maturity
ModD= years to maturity times v
Calculating MacD with an annuity
ADD PV OF MATURITY
If not annual- change n and interest rate according to the period
If annuity due → arithmetic series is n-1 periods and use annuity due for bottom

Macaulay convexity formula

Modified convexity formula

MacC convexity with zero coupon bond
MacC equals n²
PV weighted average MacD and MacC
