FM for Actuaries

180 CHAPTER 5
the sinking fund after n years is just enough to redeem the loan. Show that
( ) ( i − j a
X − X ′ n−1⌉ j
= L
1+j
a n⌉ j
)
.
5.43 Nikita takes out a 5-year loan at 8% and pays interest of $120 to the lender at
the end of every year. She also makes deposits into a sinking fund at the end
of each year for 5 years, earning an effective rate of j per annum to repay the
loan. The following is the sinking fund schedule of Nikita.
Year Sinking fund deposit Sinking fund interest Sinking fund balance
1 260.836
2
3
4
5
(a) Find j. Then fill in the missing values in the schedule and find the net
amount of interest paid to the lender.
(b) If the sinking fund is actually invested by the lender, what is the overall
yield rate of the lender?
5.44 The following is a sinking fund schedule for the accumulation of $2,000 in 6
years by annual level deposits. Fill in the missing values in the schedule.
Year Sinking fund deposit Sinking fund interest Sinking fund balance
1
2
3 885.069
4
5
6
5.45 Luke repays a debt at 6% effective with payments of $400 at the end of each
of the first 5 years, which then decreases by $20 each year until it becomes
$200 at the end of 15 years. Find the amount of the loan if the sinking fund
used to accumulate the capital earns a rate of only 5% effective.