Foundations of Mathematics 12
Kim
Ch1. Mid Chapter Summary
1. Formula for Simple Interest vs. Compound Interest
Simple Interest
Compound Interest
I =Amount of Interest
I = Prt
I=A-P
A=
A= P + I
A = P (1 + i )n





if Prt is replaced with I
Final Amount of
Investment
Future Value
Balance
Value at Maturity
Return
where
= P + Prt

interest payments (for a given term)
if factor out P

= P (1 + rt)
Note
n represents the total number of
i
represents the interest rate per
compounding period
no formula directly let you calculate A
No formula directly let you calculate I
2. Compound Interest with Different Interest Payment Period
Compounding Period
- How Often the
Interest is Paid
Number of
Interest
Payment
Per Year
n=
Total Number of
Interest Payments
(from beginning to
the end of the term)
*t=time in year
Annually
1
1t
Semi-Annually
2
2t
Quarterly
4
4t
Monthly
12
12t
Daily
365
365t
i=
Formula for future amount
Interest Rate, Per
Compounding
Period
A = P (1 + i )n
*r =annual interest
rate
𝑟
1
𝑟
2
𝑟
4
𝑟
12
𝑟
365
P (1 + 𝑟)t
𝑟
P (1 + )2t
P (1
2
𝑟
+ )4t
4
𝑟 12t
P (1 + )
12
𝑟
P (1 +
365
)12t
Foundations of Mathematics 12
Kim
3. Calculations Using TVM Solver
Access TVM Solver on TI-83: APPS 1
1
Enter
Note: For TI-83, Cash Received is a POSITVE and Cash Paid is a Negative Value (i.e. money leaving your pocket)
This is why we need to put ‘-‘ initial investment for PV)
4. Other Concepts
 Rules of 72:
 Rate of Return:
72
= Estimate Doubling Time
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 %
𝐼 (𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡)
𝑃 (𝑝𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙)