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Sinking Funds for Financial Planning

Shane wants to have Php800,000 in 5 years by depositing annually into a sinking fund earning 6% effective interest. The problem is to find the annual deposit amount. Formulas are provided to calculate the amount in the fund after any deposit period, the periodic deposit, interest earned in any period, and fund increase in any period. A sinking fund schedule table is also described that tracks these values over the deposit periods.

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Kim T
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38 views10 pages

Sinking Funds for Financial Planning

Shane wants to have Php800,000 in 5 years by depositing annually into a sinking fund earning 6% effective interest. The problem is to find the annual deposit amount. Formulas are provided to calculate the amount in the fund after any deposit period, the periodic deposit, interest earned in any period, and fund increase in any period. A sinking fund schedule table is also described that tracks these values over the deposit periods.

Uploaded by

Kim T
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Motivation

Sinking Funds
In order to have Php800,000 in 5 years, Shane
deposits an amount each year in a sinking
fund earning 6% effective. Find the annual
deposit.

Sinking Funds
In order to have Php800,000 in 5 years, Shane
deposits an amount each year in a sinking
fund earning 6% effective.

Period Beginning Interest Regular Ending


amount earned deposit amount
1
2
3
4
5

Sinking Funds
Sinking Funds

Sinking Funds
• Sinking fund – a fund-accumulation scheme
wherein the amount is generated by making
periodic deposits
• In sinking fund problems, we usually want to
find the following values:
– Periodic deposit
– Amount in the fund after any kth deposit
– Interest earned in any period
– Increase in the fund in any period

Sinking Funds
• Sinking fund schedule – a table which shows
how a target amount is completely attained
through periodic deposits as well as interests
these deposits earn in the process

Sinking Funds
Formulas:
• Amount in the fund after k deposits
(1  is )k 1
Sk  R 
 i 
• Periodic deposit
s
Sk is
R
(1 is )k 1
• Interest earned
IEk  Sk 1is

• Fund increase
INCk  Sk  Sk 1

Sinking Funds
To raise money for office space expansion, a
small business operator estimates that
Php15M will be needed in 4 ½ years. He
projects that a certain amount must be
invested every 3 months in a fund which earns
interest at 12% converted quarterly.
a) How much is the quarterly investment?
b) How much will be in the fund after the 3rd
deposit?
c) How much interest is earned on the 3rd year?
Sinking Funds
Sinking fund method of paying off a debt –
happens when the debtor pays interest
periodically and pays the principal in one lump-
sum payment at the end of the term from a
sinking fund

Formulas:
• Periodic cost (when a sinking fund is used to
pay off a debt)
is A
C  iA A
(1is) 1
n

Sinking Funds
A Php500,000 loan at 13% interest rate payable
semi-annually is to be repaid in 10 years. Find
the semi-annual expense if
a) the loan is to be amortized every 6 months
b) the loan is repaid through a sinking fund
earning at 15% compounded semi-annually.
How much does the borrower save semi-
annually by choosing the cheaper method?

Sinking Funds

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