Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
Correct Answer
$10170
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 8%
Time (t) = 10 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% × 10
= $5650 ×8/100 × 10
= 5650 × 8 × 10/100
= 45200 × 10/100
= 452000/100
= $4520
Thus, Simple Interest = $4520
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 + $4520
= $10170
Thus, Amount to be paid = $10170 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) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 8% × 10)
= $5650 + ($5650 ×8/100 × 10)
= $5650 + (5650 × 8 × 10/100)
= $5650 + (45200 × 10/100)
= $5650 + (452000/100)
= $5650 + $4520 = $10170
Thus, Amount (A) to be paid = $10170 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 10 years
= Simple interest for 1 year × 10
= $452 × 10 = $4520
Thus, Simple Interest (SI) = $4520
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $4520
= $10170
Thus, Amount to be paid = $10170 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(6) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.