Question:
If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3763
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 3%
Time (t) = 2 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) = $3550 × 3% × 2
= $3550 ×3/100 × 2
= 3550 × 3 × 2/100
= 10650 × 2/100
= 21300/100
= $213
Thus, Simple Interest = $213
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 = $3550 + $213
= $3763
Thus, Amount to be paid = $3763 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 = $3550
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3550 + ($3550 × 3% × 2)
= $3550 + ($3550 ×3/100 × 2)
= $3550 + (3550 × 3 × 2/100)
= $3550 + (10650 × 2/100)
= $3550 + (21300/100)
= $3550 + $213 = $3763
Thus, Amount (A) to be paid = $3763 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 $3550, the simple interest in 1 year
= 3/100 × 3550
= 3 × 3550/100
= 10650/100 = $106.5
Thus, simple interest for 1 year = $106.5
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $106.5 × 2 = $213
Thus, Simple Interest (SI) = $213
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $213
= $3763
Thus, Amount to be paid = $3763 Answer
Similar Questions
(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(2) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(6) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?
(10) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.