Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.
Correct Answer
$3324.5
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 3%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 3
= $3050 ×3/100 × 3
= 3050 × 3 × 3/100
= 9150 × 3/100
= 27450/100
= $274.5
Thus, Simple Interest = $274.5
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 + $274.5
= $3324.5
Thus, Amount to be paid = $3324.5 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3050 + ($3050 × 3% × 3)
= $3050 + ($3050 ×3/100 × 3)
= $3050 + (3050 × 3 × 3/100)
= $3050 + (9150 × 3/100)
= $3050 + (27450/100)
= $3050 + $274.5 = $3324.5
Thus, Amount (A) to be paid = $3324.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3050, the simple interest in 1 year
= 3/100 × 3050
= 3 × 3050/100
= 9150/100 = $91.5
Thus, simple interest for 1 year = $91.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $91.5 × 3 = $274.5
Thus, Simple Interest (SI) = $274.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $274.5
= $3324.5
Thus, Amount to be paid = $3324.5 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.
(3) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(6) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.
(10) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?