Actuary FM Exam Questions & Answers 2023/2024
Principal - ANSWER-The amount of money deposited
Simple Interest - ANSWER-Interest earned only on the original principal amount invested
Compound Interest - ANSWER-interest earned on both the principal amount and any interest already earned
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Simple Interest - ANSWER-Interest earned only on the original principal amount invested
Compound Interest - ANSWER-interest earned on both the principal amount and any interest already
earned
I(t) - ANSWER-Amount of interest earned in the t'th period, = A(t) - A(t-1)
A(t) - ANSWER-Amount function, amount of money in fund/invested at any time t
step function - ANSWER-type of amount function that isn't continuous (doesn't have non-stop accruing
interest); interest is earned only at the end of each period
Effective rate of interest : i (sub)t - ANSWER-used to measure the rate at which a deposit grows due to
interest; = I(t)/A(t-1) or (A(t) - A(t-1)) / A(t-1)
Solving for A(t) using effective rate of interest; assuming going to time-0 amount - ANSWER-A(3) = A(0)
(1+i(sub)3)(1+i(sub)2)(1+i(sub)1)
A(t) = A(0)(1+i)^t if the effective interest rate (i) is constant over all periods
annual effective rate - ANSWER-only looks at the deposit at the beginning and end of the year,
completely ignores the volatility of the deposit throughout the rest of the year
removing assumption that initial investment occurs at time-0, instead initial investment happens at time
k - ANSWER-A(t) = A(k)(1+i)^(t-k)
, This equation is if the effective interest rate (i) is constant over all periods
Present Value (PV) - ANSWER-amount the investment is currently worth
Accumulated or Future Value (AV or FV) - ANSWER-the value of the investment after a certain time
Using an amount function graph:
going from left to right - ANSWER-Accumulating
used to calculate future or accumulated values (FV or AV) using Present value (PV)
Using amount fcn graph:
going from right to left - ANSWER-discounting
used to calculate present value (PV) using future value (FV or AV)
Time Diagram - ANSWER-used to calculate Present and Accumulated Values, documented with cash
inflows and cash outflows
needs a comparison date- the common date to discount or accumulate each cash flow to
Comparison date is whatever point you are trying to calculate, if accumulating from time-0 to time-1,
time-1 is the comparison date
discount factor(v) - ANSWER-used to discount (remove) a year of interest; = 1/ (1+i)
discounting from time-3 with $3,000 to time-0 with annual effective interest rate (i) of 7.5% - ANSWER-t0
= 3,000 / ((1.075)^3)
effective rate of discount (d (sub)t) - ANSWER-the interest based on the end of the period amount
function; = I(t)/A(t) or (A(t) - A(t-1)) / A(t); only difference to effective rate of interest is the denominator
accumulating equations; using A(0) value to find A(2) value and effective interest rates/ discount rates
constant - ANSWER-A(2) = A(0)(1+i)^t
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