Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
Correct Answer
$8034
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5150 ×7/100 × 8
= 5150 × 7 × 8/100
= 36050 × 8/100
= 288400/100
= $2884
Thus, Simple Interest = $2884
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 + $2884
= $8034
Thus, Amount to be paid = $8034 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 7% × 8)
= $5150 + ($5150 ×7/100 × 8)
= $5150 + (5150 × 7 × 8/100)
= $5150 + (36050 × 8/100)
= $5150 + (288400/100)
= $5150 + $2884 = $8034
Thus, Amount (A) to be paid = $8034 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5150, the simple interest in 1 year
= 7/100 × 5150
= 7 × 5150/100
= 36050/100 = $360.5
Thus, simple interest for 1 year = $360.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $360.5 × 8 = $2884
Thus, Simple Interest (SI) = $2884
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2884
= $8034
Thus, Amount to be paid = $8034 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(4) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(6) Mark had to pay $5060 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 8% simple interest for 8 years.
(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(10) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.