simple and compound interest

1. Simple and Compound
Interest

2. Simple Interest
𝐼𝑠 = 𝑃𝑟𝑡
Where:
𝐼𝑆 = simple interest
P = principal
r = rate
t = term or time, in years

3. Maturity (Future) Value
F = P + 𝐼𝑆, or F = P(1+rt)
Where:
F = Maturity (future) value
𝐼𝑆 = simple interest
P = principal
r = rate
t = term or time, in years

4. Example:
Find the interest and maturity value if Sara deposits P20,000
at a bank for 3 years at an interest rate of 4% per year.
𝐼𝑆 = Prt
= (20,000)(.04)(3)
𝐼𝑆 = P2,400
F = P+ 𝐼𝑆
= 20,000+2400
= 22,400
F = P(1+rt)
= 20000(1+(0.04)(3))
= 22,400
or
Thus, after 3 years, the P20,000
deposited in the bank will earn an
interest of P2,400, therefore, the
money will grow to P22,400.

5. Maturity Value and Compound Interest
F = P 1 + 𝑟 𝑡
Where: P = principal or present value
F = Maturity (future) value at the end of the term
r = interest rate
t = term or time, in years

6. Compound Interest
𝐼𝑐 = F - P
Where: P = principal or present value
F = Maturity (future) value at the end of the term

7. Example 2
Find the maturity value and compound interest if P30,000 is
invested at 3% compounded annually for 6 years.
F = P 𝟏 + 𝒓 𝒕
= 30,000 1 + 0.03 6
F = 35,821.57
𝑰𝒄 = F - P
= 35,821.57 – 30,000
𝐼𝑐 = 5,821.57
Thus, P30,000 invested at 3%
compounded annually for 6
years will earn an interest of
P5,821.57. therefore the
money will grow to
P35,821.57.

8. Present Value P at compound Interest
𝑃 =
𝐹
1 + 𝑟 𝑡
= 𝐹 1 + 𝑟 −𝑡
Where: P = principal or present value
F = maturity (future) value at the end of the term
r = interest rate
t = term/time in years

9. Example
What is the present value of P50,000 due in 7 years if money
is worth 10% compounded annually?
P =
50000
1+0.1 7
P = 25,657.91
The present value is P25,657.91.

10. Example
How much money should a student place in a time deposit in a
bank that pays 1.1% compounded annually so that he will
have P200,000 after 6 years?
F = 200,000 r = 1.1% or 0.011t = 6 years
Solution:
𝑃 =
𝐹
1 + 𝑟 𝑡

11. Example
Mr. Bautista aims to have his investment grow to P500,000 in
4 years. How much should he invest in an account that pays
5% compounded annually?
F = 500,000 r = 0.05 t = 4 years
Solution:
𝑃 =
𝐹
1 + 𝑟 𝑡

12. Solve
In order to have P250,000 in 5 years, how much should you
invest if the compound interest is 12%?