Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
Correct Answer
$3622.5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 5%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 3
= $3150 ×5/100 × 3
= 3150 × 5 × 3/100
= 15750 × 3/100
= 47250/100
= $472.5
Thus, Simple Interest = $472.5
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 + $472.5
= $3622.5
Thus, Amount to be paid = $3622.5 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) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 5% × 3)
= $3150 + ($3150 ×5/100 × 3)
= $3150 + (3150 × 5 × 3/100)
= $3150 + (15750 × 3/100)
= $3150 + (47250/100)
= $3150 + $472.5 = $3622.5
Thus, Amount (A) to be paid = $3622.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3150, the simple interest in 1 year
= 5/100 × 3150
= 5 × 3150/100
= 15750/100 = $157.5
Thus, simple interest for 1 year = $157.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $157.5 × 3 = $472.5
Thus, Simple Interest (SI) = $472.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $472.5
= $3622.5
Thus, Amount to be paid = $3622.5 Answer
Similar Questions
(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(3) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.
(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(8) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.