Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.
Correct Answer
$8642
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5800 × 7% × 7
= $5800 ×7/100 × 7
= 5800 × 7 × 7/100
= 40600 × 7/100
= 284200/100
= $2842
Thus, Simple Interest = $2842
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 = $5800 + $2842
= $8642
Thus, Amount to be paid = $8642 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 = $5800
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5800 + ($5800 × 7% × 7)
= $5800 + ($5800 ×7/100 × 7)
= $5800 + (5800 × 7 × 7/100)
= $5800 + (40600 × 7/100)
= $5800 + (284200/100)
= $5800 + $2842 = $8642
Thus, Amount (A) to be paid = $8642 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 $5800, the simple interest in 1 year
= 7/100 × 5800
= 7 × 5800/100
= 40600/100 = $406
Thus, simple interest for 1 year = $406
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $406 × 7 = $2842
Thus, Simple Interest (SI) = $2842
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $2842
= $8642
Thus, Amount to be paid = $8642 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(4) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(9) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?
(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.