Question:
Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
Correct Answer
$9690
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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) = $5700 × 7% × 10
= $5700 ×7/100 × 10
= 5700 × 7 × 10/100
= 39900 × 10/100
= 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 10)
= $5700 + ($5700 ×7/100 × 10)
= $5700 + (5700 × 7 × 10/100)
= $5700 + (39900 × 10/100)
= $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 = 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 $5700, the simple interest in 1 year
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = $399
Thus, simple interest for 1 year = $399
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $399 × 10 = $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) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
(9) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.