Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
Correct Answer
$6780
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5650 ×2/100 × 10
= 5650 × 2 × 10/100
= 11300 × 10/100
= 113000/100
= $1130
Thus, Simple Interest = $1130
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 + $1130
= $6780
Thus, Amount to be paid = $6780 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 2% × 10)
= $5650 + ($5650 ×2/100 × 10)
= $5650 + (5650 × 2 × 10/100)
= $5650 + (11300 × 10/100)
= $5650 + (113000/100)
= $5650 + $1130 = $6780
Thus, Amount (A) to be paid = $6780 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5650, the simple interest in 1 year
= 2/100 × 5650
= 2 × 5650/100
= 11300/100 = $113
Thus, simple interest for 1 year = $113
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $113 × 10 = $1130
Thus, Simple Interest (SI) = $1130
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $1130
= $6780
Thus, Amount to be paid = $6780 Answer
Similar Questions
(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.
(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(5) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(7) James had to pay $3360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.