Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
Correct Answer
$3782
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 8%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $3050 × 8% × 3
= $3050 ×8/100 × 3
= 3050 × 8 × 3/100
= 24400 × 3/100
= 73200/100
= $732
Thus, Simple Interest = $732
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $732
= $3782
Thus, Amount to be paid = $3782 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $3050
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 3 years
Thus, Amount (A)
= $3050 + ($3050 × 8% × 3)
= $3050 + ($3050 ×8/100 × 3)
= $3050 + (3050 × 8 × 3/100)
= $3050 + (24400 × 3/100)
= $3050 + (73200/100)
= $3050 + $732 = $3782
Thus, Amount (A) to be paid = $3782 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3050, the simple interest in 1 year
= 8/100 × 3050
= 8 × 3050/100
= 24400/100 = $244
Thus, simple interest for 1 year = $244
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $244 × 3 = $732
Thus, Simple Interest (SI) = $732
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $732
= $3782
Thus, Amount to be paid = $3782 Answer
Similar Questions
(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(2) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.
(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(8) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.