Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
Correct Answer
$7622
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5150 ×6/100 × 8
= 5150 × 6 × 8/100
= 30900 × 8/100
= 247200/100
= $2472
Thus, Simple Interest = $2472
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 + $2472
= $7622
Thus, Amount to be paid = $7622 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 6% × 8)
= $5150 + ($5150 ×6/100 × 8)
= $5150 + (5150 × 6 × 8/100)
= $5150 + (30900 × 8/100)
= $5150 + (247200/100)
= $5150 + $2472 = $7622
Thus, Amount (A) to be paid = $7622 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5150, the simple interest in 1 year
= 6/100 × 5150
= 6 × 5150/100
= 30900/100 = $309
Thus, simple interest for 1 year = $309
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $309 × 8 = $2472
Thus, Simple Interest (SI) = $2472
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2472
= $7622
Thus, Amount to be paid = $7622 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) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
(6) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(10) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.