Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
Correct Answer
$4148
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 9%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 4
= $3050 ×9/100 × 4
= 3050 × 9 × 4/100
= 27450 × 4/100
= 109800/100
= $1098
Thus, Simple Interest = $1098
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 + $1098
= $4148
Thus, Amount to be paid = $4148 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) = 9%
And, Time (t) = 4 years
Thus, Amount (A)
= $3050 + ($3050 × 9% × 4)
= $3050 + ($3050 ×9/100 × 4)
= $3050 + (3050 × 9 × 4/100)
= $3050 + (27450 × 4/100)
= $3050 + (109800/100)
= $3050 + $1098 = $4148
Thus, Amount (A) to be paid = $4148 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3050, the simple interest in 1 year
= 9/100 × 3050
= 9 × 3050/100
= 27450/100 = $274.5
Thus, simple interest for 1 year = $274.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $274.5 × 4 = $1098
Thus, Simple Interest (SI) = $1098
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $1098
= $4148
Thus, Amount to be paid = $4148 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(2) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(4) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.
(6) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.
(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.