Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
Correct Answer
$3528
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 3%
Time (t) = 4 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) = $3150 × 3% × 4
= $3150 ×3/100 × 4
= 3150 × 3 × 4/100
= 9450 × 4/100
= 37800/100
= $378
Thus, Simple Interest = $378
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 + $378
= $3528
Thus, Amount to be paid = $3528 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) = 3%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 3% × 4)
= $3150 + ($3150 ×3/100 × 4)
= $3150 + (3150 × 3 × 4/100)
= $3150 + (9450 × 4/100)
= $3150 + (37800/100)
= $3150 + $378 = $3528
Thus, Amount (A) to be paid = $3528 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 $3150, the simple interest in 1 year
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = $94.5
Thus, simple interest for 1 year = $94.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $94.5 × 4 = $378
Thus, Simple Interest (SI) = $378
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $378
= $3528
Thus, Amount to be paid = $3528 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.
(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(9) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.