Simple Interest

SIMPLE INTEREST Since this section involves what can happen to your money, it should be of INTEREST to you!

Objectives: At the end of the lesson, the learner is able to compute interest, maturity value and present value in simple interest environment and solve problems involving simple interest.

IMPLE INTEREST DEFINITION Interest paid on the principal only

and NOT on any accumulated interest

IMPLE INTEREST FORMULA Interest paid

Annual interest rate

I = PRT s

Principal (Amount of money invested or borrowed)

Time (in years)

Using the formula in simple interest, complete the table by finding the unknown:

If you invested ₱2,000.00 in an account that paid simple interest of 4%, find the interest earned after 𝟏 1 years. 𝟐

I = PRT I = (2,000)(0.04)(1.5) I = ₱ 120

2. A bank offers 0.25% annual simple interest rate for a particular deposit. How much interest will be earned if 1 million pesos is deposited in this savings account for 1 year?

Solving for Time Example 1.

If you invested ₱300.00 in an account that paid simple interest, find how long you’d need to leave it in at 4% interest to make ₱15.00. enter in formula as a decimal

I = PRT 15 = (300)(0.04)T 1.25 yrs = T

Example 2.

The interest on a loan of ₱ 1,800 is ₱20. If the rate of interest is 5%, when is the loan due? Given:

t=

𝐼 t = 0.22 years (1,800)(0.05)

P = ₱ 1,800 or 0.22 years x 12months = 2.64 months I = ₱20 R = 5% or 0.22 x 365 days = 80.3 days Req’d: t

Example 3.

How long will it take ₱ 305,000 to earn ₱ 325 at 4% ?

Solving for Principal Example:

When invested at an annual interest rate of 7%, an amount earned ₱ 11,200 of simple interest in two years. How much was originally invested?

Example 2:

If a nine-month term deposit at a bank a simple interest rate of 9% per annum, how much will have to be deposited to earn ₱ 225 of interest? Given: t= 9 months or 0.75 years r = 9% or 0.09 I = ₱ 225

P=

𝐼 𝑟𝑡

P=

225 (0.09)(0.75)

P =₱ 3,333.33

Example 3:

The repayment on a loan was ₱13,670. If the loan was for 15 months at 12% interest a year, how much was the principal?

Solving for Rate Example:

If an entrepreneur applies for a loan amounting to ₱ 500,000 in a bank, the simple interest of which is ₱ 157,500 for 3 years, what interest rate is being charged?

Example 2:

The interest on a loan of ₱ 2,500 is ₱ 60. If the loan is to be paid after 180 days, what is the rate of interest charged? Given: P = ₱ 2,500 I = ₱ 60

Solution: r=

𝑰 𝑷𝒕

𝟏𝟖𝟎 t= 𝟑𝟔𝟓

r=

Req’d: r

r = 0.049 or 4.9%

𝟔𝟎 (𝟐𝟓𝟎𝟎)(𝟎.𝟒𝟗)

Example 3

Interest of ₱1,904 was charged on a loan of ₱6,800 for 4 years. What simple annual rate of interest was charged on the loan? Solution: Given: I = ₱1,904 P = ₱6,800 t = 4 years

r= r=

𝑰 𝑷𝒕 𝟏,𝟗𝟎𝟒 𝟔𝟖𝟎𝟎 (𝟒)

r = 0.07 or 7%

Maturity Value / Future Value

The Value of an asset at a specific date or amount after t years

Variables for Maturity Value

Future Value

Amount

Calculating Maturity Value / Future Value

or

Example

If you invested ₱200.00 in an account that paid simple 1 interest of 4%, find the maturity value after 1 years. 2

Example If you invested ₱200.00 in an account that paid simple interest of 4%, find the maturity value 1 after 1 years. 2

FV = Principal + Interest FV = P + I FV = P + PRT FV = 200 + (200)(.04)(1.5) FV = 200 + 12 FV = ₱ 212

Example 2. Find the maturity value if 1 million pesos is deposited in a bank at an annual simple interest rate of 0.25% after a. 1 year b. Maturity after 5 years b. 5 years Is = PRT Given : P = 1,000,000 r = 0.25% = 0.0025

a. Maturity or future value F after 1 year F = P (1 + rt) F = 1,000,000 (1 +0.0025(1)) F = ₱ 1,002,500

Is = 1,000,000(0.0025)(5) Is = ₱ 12,500 F = P + Is F = 1,000,000 + 12,500 F = ₱ 1,012,500

Example 3.

Angel deposited ₱ 20,000 in a bank that pays 0.5% simple interest. How much will be her money after 6 years?

Answer: ₱ 20,600