Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
Correct Answer
$6498
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 2%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5700 × 2% × 7
= $5700 ×2/100 × 7
= 5700 × 2 × 7/100
= 11400 × 7/100
= 79800/100
= $798
Thus, Simple Interest = $798
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 = $5700 + $798
= $6498
Thus, Amount to be paid = $6498 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 = $5700
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 2% × 7)
= $5700 + ($5700 ×2/100 × 7)
= $5700 + (5700 × 2 × 7/100)
= $5700 + (11400 × 7/100)
= $5700 + (79800/100)
= $5700 + $798 = $6498
Thus, Amount (A) to be paid = $6498 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5700, the simple interest in 1 year
= 2/100 × 5700
= 2 × 5700/100
= 11400/100 = $114
Thus, simple interest for 1 year = $114
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $114 × 7 = $798
Thus, Simple Interest (SI) = $798
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $798
= $6498
Thus, Amount to be paid = $6498 Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.
(2) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(3) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(4) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(5) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.