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) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(5) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.