Question:
Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
Correct Answer
$7748
Solution And Explanation
Solution
Given,
Principal (P) = $5200
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) = $5200 × 7% × 7
= $5200 ×7/100 × 7
= 5200 × 7 × 7/100
= 36400 × 7/100
= 254800/100
= $2548
Thus, Simple Interest = $2548
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 + $2548
= $7748
Thus, Amount to be paid = $7748 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) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5200 + ($5200 × 7% × 7)
= $5200 + ($5200 ×7/100 × 7)
= $5200 + (5200 × 7 × 7/100)
= $5200 + (36400 × 7/100)
= $5200 + (254800/100)
= $5200 + $2548 = $7748
Thus, Amount (A) to be paid = $7748 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 $5200, the simple interest in 1 year
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = $364
Thus, simple interest for 1 year = $364
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $364 × 7 = $2548
Thus, Simple Interest (SI) = $2548
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2548
= $7748
Thus, Amount to be paid = $7748 Answer
Similar Questions
(1) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.
(4) How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(6) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(8) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.
(10) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.