Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.
Correct Answer
$9266
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5650 × 8% × 8
= $5650 ×8/100 × 8
= 5650 × 8 × 8/100
= 45200 × 8/100
= 361600/100
= $3616
Thus, Simple Interest = $3616
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 = $5650 + $3616
= $9266
Thus, Amount to be paid = $9266 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 = $5650
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 8% × 8)
= $5650 + ($5650 ×8/100 × 8)
= $5650 + (5650 × 8 × 8/100)
= $5650 + (45200 × 8/100)
= $5650 + (361600/100)
= $5650 + $3616 = $9266
Thus, Amount (A) to be paid = $9266 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5650, the simple interest in 1 year
= 8/100 × 5650
= 8 × 5650/100
= 45200/100 = $452
Thus, simple interest for 1 year = $452
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $452 × 8 = $3616
Thus, Simple Interest (SI) = $3616
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3616
= $9266
Thus, Amount to be paid = $9266 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(2) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?
(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.
(6) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(8) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.