Two Methods of Calculating Simple Interest and Maturity Value

Method 1: Exact Interest Used by Federal Reserve banks and the federal government

This method assumes that number of days in a year is 365 days
Time = Exact number of days ÷ 365
Example: On March 4, Amy borrowed $40,000 at 4%. Interest and principal are due on July 6.
Question: Find the interest and mature value
Answer: I = P × R × T = $40,000 × 0.04 × 124 / 365 = $543.56
MV = P + I = $40,000 + $543.56 = $40,543.56

Method 2 : Ordinary Interest (Banker's Rule)

This method assumes that number of days in a year is 360 days
Time = Exact number of days ÷ 360
Example: On March 4, Mary borrowed $40,000 at 4%. Interest and principal are due on July 6.
Question: Find the interest and mature value
Answer: I = P × R × T = $40,000 × 0.04 × 124 / 360 = $551.11
MV = P + I = $40,000 + $551.11 = $40,551.11

Example: Adam paid the bank $23.55 interest at 7.5% for 75 days.
How much did Henry borrow using the ordinary interest method?
Answer: P = I ÷ (Rate × Time) = $23.55 ÷ (0.075 × (75 / 360) = $1,507.20
Interest (I) = Principal (P) × Rate (R) × Time (T)
Check 23.55 = 1,507.20 × 0.075 × (75 / 360)

More exercises

The following formula will used in the next exercises: Interest (I) = Principal (P) x Rate (R) x Time (T); MV = P + I

Exercise 1: Calculate the simple interest and maturity value for the following problem (Round to the nearest cent as needed):
Principal = $8,000; Interest Rate = 3.50%; Time = 20 months;
Answer:
I = $8,000 × 0.035 × (20 ÷ 12) = $466.66;
MV = P + I = $8,000 + $466.66 = $8466.66

Exercise 2: Calculate the simple interest and maturity value using ordinary interest for the following problem (Round to the nearest cent as needed):
Principal = $2,000; Interest Rate = 5%; Date borrowed: March 8; Date repayed: June 9;
Answer:
T = Exact number of days ÷ 360 = 160 − 67 = 93 days;
I = $2,000 × 0.05 × (93 / 360) = $25.83
MV = P + I = $2,000 + $25.83 = $2,025.83

Exercise 3: Use the same data of Exercise 2 and the exact interest to find simple interest and maturity value.
Answer:
T = Exact number of days ÷ 360 = 160 − 67 = 93 days;
I = $2,000 × 0.05 × (93 / 365) = $25.48
MV = P + I = $2,000 + $25.48 = $2,025.48

Exercise 4: Solve for the time in month or years where:
P = $500; Interest rate = 7%; Simple interest = $150.00;
Answer:
T = $150.00 / ($500.00 × 0.07) = 4.28 years

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Date of last modification: March 11, 2019