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) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.
(7) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(9) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.