Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
Correct Answer
$3906
Solution And Explanation
Solution
Given,
Principal (P) = $3150
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) = $3150 × 8% × 3
= $3150 ×8/100 × 3
= 3150 × 8 × 3/100
= 25200 × 3/100
= 75600/100
= $756
Thus, Simple Interest = $756
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 = $3150 + $756
= $3906
Thus, Amount to be paid = $3906 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 = $3150
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 8% × 3)
= $3150 + ($3150 ×8/100 × 3)
= $3150 + (3150 × 8 × 3/100)
= $3150 + (25200 × 3/100)
= $3150 + (75600/100)
= $3150 + $756 = $3906
Thus, Amount (A) to be paid = $3906 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 $3150, the simple interest in 1 year
= 8/100 × 3150
= 8 × 3150/100
= 25200/100 = $252
Thus, simple interest for 1 year = $252
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $252 × 3 = $756
Thus, Simple Interest (SI) = $756
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $756
= $3906
Thus, Amount to be paid = $3906 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(2) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(3) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.
(6) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) 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.
(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.