Summary Theory of interest 152 notes

THEORY OF INTEREST 152

Overview – ways to calculate interest
1. Simple interest 𝑖 ® 1.1, hand, 2%
$ (")
2. Compound interest 𝑖; 𝑖 (") ; "
® 1.5, 1.7, 1.9, 2.2, 2.8, calculator, 90%
% & $ (") &
3. Discount 𝑑 ® " = ' ; "
=(;D=S-𝑘
4. Force of interest 𝑟 ® 1.10, hand, 3%

CHAPTER 1 – INTEREST CONCEPTS, SIMPLE AND COMPOUND INTEREST

1.2 Basic concepts

Equation Description Calculator
K Capital amount PV
S Accumulated amount FV
𝑖 Effective interest rate per year
(")
I/YR
𝑖 Nominal interest rate per year
No. times per year interest is
𝑚 P/YR
earned/compounded
𝑛 No. of years
N
N No. interest periods (𝑛 x 𝑚)

• +R = receiving money
Þ Taking out a loan
Þ Withdrawing money from an account
• -R = giving money
Þ Making a loan payment
Þ Investing money into an account

1.3.1 Simple Interest

• No interest on interest
• Solve equation mathematically

S = K (1 + 𝑖𝑛)
S = K + K𝑖𝑛

S = K [1 + (number of periods) x (interest rate per unit per period)]

Interest earned = amount received – amount invested
Interest earned = K𝑖𝑛

, 1.3.2 Compound Interest

• Interest on interest
• Just put question into notation equation, not solving mathematically
• Solve using financial calculator Tine Value of Money functions

𝑚𝑥𝑛 𝑖 (") K S (white)




𝑛 𝑚 (orange)

Bracket notation: have a present value, need its future value

S = K (1 + 𝑖)) ® 𝑖 effective per year; 𝑛 years (not used often)

"+)
$ (")
S = K ,1 + "
- ® 𝑖 (") nominal per year; 𝑛 years; 𝑚 interest periods per year

V notation: have a future value; need its present value

,
K = (-.$)$ = 𝑆𝑣 )$ ® 𝑖 effective per year; 𝑛 years (not used often)

"+)
K = 𝑆𝑣 %(") ® 𝑖 (") nominal per year; 𝑛 years; 𝑚 interest periods per year
"



Compounding per year

• Nominal interest rates – how frequent interest is compounded in a year
• 𝑖 (") (general)
Þ 𝑖 – I/YR
Þ 𝑚 – P/YR
• 𝑖 (-) VS 𝑖 (/)
Þ the more times interest is compounded per year the more interest will be
earned
$ (&')
• -/
= effective interest rate per month (used in calculations)