Question:
Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
Correct Answer
$5928
Solution And Explanation
Solution
Given,
Principal (P) = $5200
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) = $5200 × 2% × 7
= $5200 ×2/100 × 7
= 5200 × 2 × 7/100
= 10400 × 7/100
= 72800/100
= $728
Thus, Simple Interest = $728
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 = $5200 + $728
= $5928
Thus, Amount to be paid = $5928 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 = $5200
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 7 years
Thus, Amount (A)
= $5200 + ($5200 × 2% × 7)
= $5200 + ($5200 ×2/100 × 7)
= $5200 + (5200 × 2 × 7/100)
= $5200 + (10400 × 7/100)
= $5200 + (72800/100)
= $5200 + $728 = $5928
Thus, Amount (A) to be paid = $5928 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 $5200, the simple interest in 1 year
= 2/100 × 5200
= 2 × 5200/100
= 10400/100 = $104
Thus, simple interest for 1 year = $104
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $104 × 7 = $728
Thus, Simple Interest (SI) = $728
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $728
= $5928
Thus, Amount to be paid = $5928 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?
(7) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.
(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(9) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.