Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
Correct Answer
$9690
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5700 ×10/100 × 7
= 5700 × 10 × 7/100
= 57000 × 7/100
= 399000/100
= $3990
Thus, Simple Interest = $3990
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 + $3990
= $9690
Thus, Amount to be paid = $9690 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 10% × 7)
= $5700 + ($5700 ×10/100 × 7)
= $5700 + (5700 × 10 × 7/100)
= $5700 + (57000 × 7/100)
= $5700 + (399000/100)
= $5700 + $3990 = $9690
Thus, Amount (A) to be paid = $9690 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5700, the simple interest in 1 year
= 10/100 × 5700
= 10 × 5700/100
= 57000/100 = $570
Thus, simple interest for 1 year = $570
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $570 × 7 = $3990
Thus, Simple Interest (SI) = $3990
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $3990
= $9690
Thus, Amount to be paid = $9690 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(6) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(8) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(9) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.