Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
Correct Answer
$7210
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5150 × 4% × 10
= $5150 ×4/100 × 10
= 5150 × 4 × 10/100
= 20600 × 10/100
= 206000/100
= $2060
Thus, Simple Interest = $2060
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 = $5150 + $2060
= $7210
Thus, Amount to be paid = $7210 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 = $5150
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 4% × 10)
= $5150 + ($5150 ×4/100 × 10)
= $5150 + (5150 × 4 × 10/100)
= $5150 + (20600 × 10/100)
= $5150 + (206000/100)
= $5150 + $2060 = $7210
Thus, Amount (A) to be paid = $7210 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5150, the simple interest in 1 year
= 4/100 × 5150
= 4 × 5150/100
= 20600/100 = $206
Thus, simple interest for 1 year = $206
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $206 × 10 = $2060
Thus, Simple Interest (SI) = $2060
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2060
= $7210
Thus, Amount to be paid = $7210 Answer
Similar Questions
(1) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?
(2) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.
(9) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.