Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
Correct Answer
$6386
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 3%
Time (t) = 8 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) = $5150 × 3% × 8
= $5150 ×3/100 × 8
= 5150 × 3 × 8/100
= 15450 × 8/100
= 123600/100
= $1236
Thus, Simple Interest = $1236
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 = $5150 + $1236
= $6386
Thus, Amount to be paid = $6386 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 = $5150
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 3% × 8)
= $5150 + ($5150 ×3/100 × 8)
= $5150 + (5150 × 3 × 8/100)
= $5150 + (15450 × 8/100)
= $5150 + (123600/100)
= $5150 + $1236 = $6386
Thus, Amount (A) to be paid = $6386 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 $5150, the simple interest in 1 year
= 3/100 × 5150
= 3 × 5150/100
= 15450/100 = $154.5
Thus, simple interest for 1 year = $154.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $154.5 × 8 = $1236
Thus, Simple Interest (SI) = $1236
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1236
= $6386
Thus, Amount to be paid = $6386 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(3) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(6) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(9) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.
(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.