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) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(5) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.
(7) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.
(9) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(10) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.