Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
Correct Answer
$4026
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 8%
Time (t) = 4 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% × 4
= $3050 ×8/100 × 4
= 3050 × 8 × 4/100
= 24400 × 4/100
= 97600/100
= $976
Thus, Simple Interest = $976
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 + $976
= $4026
Thus, Amount to be paid = $4026 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) = 4 years
Thus, Amount (A)
= $3050 + ($3050 × 8% × 4)
= $3050 + ($3050 ×8/100 × 4)
= $3050 + (3050 × 8 × 4/100)
= $3050 + (24400 × 4/100)
= $3050 + (97600/100)
= $3050 + $976 = $4026
Thus, Amount (A) to be paid = $4026 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 4 years
= Simple interest for 1 year × 4
= $244 × 4 = $976
Thus, Simple Interest (SI) = $976
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $976
= $4026
Thus, Amount to be paid = $4026 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(2) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(4) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.
(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(6) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.