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Interest
Annuities
Yield Rates / miscellaneous
Amortization / Sinking Funds
Bonds / Duration
100
the discount rate expressed in terms of interest rates
d = i / (1+i)
100
What is the annuity immediate formula? (a angle n = ? )
a angle n = (1- v ^ n ) / i
100
What are spot rates?
The yield on a zero coupon bond.
100
Say you got out a 10-year loan for 1k at an interest rate of 5%. If you were asked to calculate your outstanding balance at year 5 how would you approach this?
Adequate description of either prospective or retrospective methods.
100
What is the formula for the price of a bond?
price = fr a angel n + f v^n
200
Force of interest expressed in terms of interest rates?
delta = ln(1+i)
200
annuity due expressed in terms of annuity immediate? (a double dot angle n = X a angle n -- what is x? )
a double dot angle n = (1+i) a angle n
200
What's the formula for the forward rate from time 1 to 2 in terms of spot rates.
2-year spot rate ^2 / 1-year spot rate
200
Describe a sinking fund? What affects does it have on the computation of present value ?
In a sinking fund, one takes out the interest from one account and stores it into another account. Usually the other account has a different interest rate. This would make it so that we would discount at two different rates.
200
If a bond is sold at a premium, what does this say about the interest rate relative to the coupon rate.
i < r
300
for an accumulation function a(t), what is the force of interest?
delta = a'(t)/a(t)
300
What is the formula for a geometrically increasing annuity? Use the notation g, where g = the percentage increase every year.
a angle n = (1- v^n) / i - g. v = (1+g/1+i)
300
A discount electronics store advertises the following financing arrangement: "We don't offer you confusing interest rates. We'll just divide your total cost by 10 and you can pay us that amount each month for a year." The first payment is due on the date of sale and the remaining eleven payments at the monthly intervals thereafter. Calculate the effective annual interest rate the store's customers are paying on their loans.
Approximately 51.2%
300
When amortizing a loan, what is the formula for the amount of principal paid on the loan at time k.
principal repaid = v ^n-k+1
300
what is the formula for mac duration ?
(Ia) angle n / a angle n. or the weighted sums of the cash flows over the price.
400
A fairly smart actuary is offered the following rates on a loan: 1. X% nominal annual rate of interest compounded monthly 2. X$ annual effective rate of interest Which rate does the FSA take?
2!
400
What is the present value formula for an arithemetically increasing perpetuity? answer with the notation P and Q where P = first payment and Q = the increasing amount.
(Ia) angle infinity = P/i + Q/(i^2). Where P is the first pay meant and Q is the increasing amount.
400
You are given the following term structure of interest rates. year 1 the spot rate = 5% year 2 the spot rate = 5.75% year 3 the spot rate = 6.25% year 4 the spot rate = 6.5% Calculate 1000(Da) angel 4 rounded to the nearest 100.
8900
400
An investor wishes to accumulate 1,000 at the end of 10 years by making level deposits at the end of each year. The deposits earn a 12% annual effective rate of interest paid at the end of each year. The interest is immediately reinvested into another bank account at an annual effective interest rate of 12%. Calculate the level deposit?
Approximately $57.00
400
given you bought a 20-year bond that is callable after year 15 at a discount that provides a yield of at least 5%. At what time t would you take the present value using this yield rate.
Year 20.
500
The force of interest is delta sub t = .02t, where t is the number of years from jan 1,2001. If $1.00 is invested on January 1, 2003, how much is in the fund on January 1, 2008?
e^(.45)
500
A perpetuity pays 1 at the end of year 1, 2 at the end of year 2, 3 at the end of year 3, and so on. The present value of this perpetuity is 420. Calculate the annual effective rate of interest.
5%
500
An annuity- immediate has the following payments: 10, 20, 30, 40, 50, 40, 30, 20, 10 Which of the following expressions represents the present value of the annuity A) 10 a angle 5 a angle 5 B) 10 a angle 5 a double dot angle 5 C) 10 a angle 5 a angle 4 D) 10 a angle 5 a double dot angle 4 E) 10(Ia) angle 5 + 10 (Da) angle 4
B
500
A bank customer takes out a loan of 500 with a 16% nominal interest rate convertible quarterly. The customer makes payments of 20 at the end of each quarter. Calculate the amount of principal in the fourth payment.
0 dollars
500
John purchased three bonds to form a portfolio as follows: Bond A has semi-annual coupons at 4%k, a duration of 21.46, and was purchased for 980. Bond B is a 15-year bond with a duration of 12.35 years and was purchased for 1015. Bond C has a duration of 16.67 years and was purchased for 1000. Calculate the duration of the portfolio at the time of purchase?
16.77 Years