Question:
If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3276
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 2%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 2
= $3150 ×2/100 × 2
= 3150 × 2 × 2/100
= 6300 × 2/100
= 12600/100
= $126
Thus, Simple Interest = $126
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 + $126
= $3276
Thus, Amount to be paid = $3276 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) = 2%
And, Time (t) = 2 years
Thus, Amount (A)
= $3150 + ($3150 × 2% × 2)
= $3150 + ($3150 ×2/100 × 2)
= $3150 + (3150 × 2 × 2/100)
= $3150 + (6300 × 2/100)
= $3150 + (12600/100)
= $3150 + $126 = $3276
Thus, Amount (A) to be paid = $3276 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest in 1 year = $2
∴ For $1, the simple interest in 1 year = 2/100
∴ For $3150, the simple interest in 1 year
= 2/100 × 3150
= 2 × 3150/100
= 6300/100 = $63
Thus, simple interest in 1 year = $63
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $63 × 2 = $126
Thus, Simple Interest (SI) = $126
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $126
= $3276
Thus, Amount to be paid = $3276 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(2) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
(4) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(5) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(7) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
(8) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.