Problems in solving compound interest

1. Compound Interest
It is the amount earned
for one year calculated
multiplying the Principal
by the interest Rate.
Interest is computed on
the principal and also
the accumulated
interest.

2. • Ella and Thelma each invest 10,000 for two
years, but under different schemes. Ella’s earns
2% of 10,000 the first year, which is 200, then
another 200 the second year. Thelma earns 2%
of 10,000 the first year, which is 200, same as
Ella’s. But during the second year, she earns
2% of 10,000 and 2% of the 200 also.
1.How much does Ella and Thelma have to
their respective account after 2 years?
2. What is the difference?
Answer: Ella- 10,400 Thelma- 10,404

3. • Many savings account pay compound
interest. In this case, the interest is added
to the account at regular intervals, and the
sum becomes the new basis for
computing interest.
• Maturity Value (future)compound interest
𝐹 = 𝑃 1 + 𝑟 𝑡
P= Principal
F= Maturity(Future) value at the end of the term
R=Interest Rate
T=term/time in years

4. The Following table shows the amount at the end
of each year if Principal is invested at an annual
interest rate r compounded annually.P=100,000
and r=5%
Year(t) Principal=P
Rate=r
compounded annually
Principal=100,000
Rate=5%
Compounded
annually
1 𝑃 1 + 𝑟 = 𝑃(1 + 𝑟) 105,000
2 𝑃 1 + 𝑟 1 + 𝑟 = 𝑃 1 + 𝑟 2 110,250
3 𝑃 1 + 𝑟 2 1 + 𝑟 = 𝑃 1 + 𝑟 3 121,550.63
4 𝑃 1 + 𝑟 3 1 + 𝑟 = 𝑃 1 + 𝑟 4 127,628.16
Show Solution on the Board

5. • Compound Interest
» 𝐼𝑐 = F − 𝑃
• Example:
• Find the maturity value and the compound
interest if 10,000 is compounded annually at an
investment rate of 2% in 5years.
a. Maturity value
b. Compound interest
Answer: 73, 872.77
23, 872.00

6. • Present Value (P)compound interest
P=
𝐹
1+𝑟 𝑡
P= Principal
F= Maturity(Future) value at the end of the term
R=Interest Rate
T=term/time in years
Example: What is the present value of 50,000 due in 7 years if
money is worth 10% compounded annually?
Answer: 25,657.91

7. 1. Find the maturity value and interest if
50,000 is invested at 5% compound annually for
8years.
a. Maturity value
b. Compound interest
2. 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
200,000 after 6 years?
3. Complete the table
Christian deposited 5,000 in a bank that pays
2% compounded annually.

8. • Quiz 2
1. Suppose your father deposited in your bank account 10,000 at
annual interest rate of 0.5% compounded yearly when you
graduate from kindergarten and did not get the amount until
you finish Grade 12. How much will you have in your bank
account after 12 years?
2. A saving account in a bank yields 0.25 % compound interest
annually, Accumulated(Find the future value)25,000 for 4
years in this saving account.
3. In a certain bank, Angel invested 8,000 in a time deposit that
pays 0.5% compound interest in a year. How much will be her
money after 6 years? How much interest will she gain?
Complete the table: