FM for Actuaries

Rates of Return 141
Assume all investments are made at the beginning of the year, and let
M1 = the total interest credited in the period 2013 through 2016 for an
investment in 2009,
M2 = the total interest credited in the period 2013 through 2016 for an
investment in 2013,
M3 = the total interest credited in the period 2013 through 2016 for an
investment in 2013, if the balance is withdrawn at the end of every year
and re-invested in the fund as new money in the following year.
Given that M1 =M2 =M3, find the two missing rates, X and Z, inthe
above table.
4.34 Find the investment-year rates and the portfolio rate credited in calendar year
2016 in Table 4.2.
4.35 An investment of $500 is made at the beginning of 2013 in the fund crediting
interest according to Table 4.2. Find the total interest credited in calender
years 2015 through 2017 inclusive.
4.36 You invest in the fund crediting interest according to Table 4.2 at the beginning
of 2012 for two years and then withdraw and reinvest the money at the
beginning of 2014 for two more years. Find the equivalent level effective
interest rate for your 4-year holding period.
4.37 Find ¨s 3⌉
using Table 4.2, assuming that the first payment is made in the
beginning of 2013 and that there is no withdrawal from the fund.
4.38 Consider the investment fund in Table 4.2. An investment of $1,000 at the
beginning of 2011 has an accumulated value of $1,220 at the beginning of
2015. At the end of 2017, the money is withdrawn. Find the equivalent level
effective rate of interest over the investment horizon.
4.39 Consider a fund which earns interest according to Table 4.2 and assume that
the force of interest over each year is constant. You invest $1,000 in the
beginning of 2014 and withdraw the investment after two and a half years.
Find the amount of interest credited.