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) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(4) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.