Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.
Correct Answer
$8094
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7
= $5700 ×6/100 × 7
= 5700 × 6 × 7/100
= 34200 × 7/100
= 239400/100
= $2394
Thus, Simple Interest = $2394
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 + $2394
= $8094
Thus, Amount to be paid = $8094 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 6% × 7)
= $5700 + ($5700 ×6/100 × 7)
= $5700 + (5700 × 6 × 7/100)
= $5700 + (34200 × 7/100)
= $5700 + (239400/100)
= $5700 + $2394 = $8094
Thus, Amount (A) to be paid = $8094 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5700, the simple interest in 1 year
= 6/100 × 5700
= 6 × 5700/100
= 34200/100 = $342
Thus, simple interest for 1 year = $342
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $342 × 7 = $2394
Thus, Simple Interest (SI) = $2394
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2394
= $8094
Thus, Amount to be paid = $8094 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(6) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(8) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.