Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
Correct Answer
$10700
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 10%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5350 × 10% × 10
= $5350 ×10/100 × 10
= 5350 × 10 × 10/100
= 53500 × 10/100
= 535000/100
= $5350
Thus, Simple Interest = $5350
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 = $5350 + $5350
= $10700
Thus, Amount to be paid = $10700 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 = $5350
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 10% × 10)
= $5350 + ($5350 ×10/100 × 10)
= $5350 + (5350 × 10 × 10/100)
= $5350 + (53500 × 10/100)
= $5350 + (535000/100)
= $5350 + $5350 = $10700
Thus, Amount (A) to be paid = $10700 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5350, the simple interest in 1 year
= 10/100 × 5350
= 10 × 5350/100
= 53500/100 = $535
Thus, simple interest for 1 year = $535
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $535 × 10 = $5350
Thus, Simple Interest (SI) = $5350
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $5350
= $10700
Thus, Amount to be paid = $10700 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(3) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
(5) Patricia took a loan of $4300 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.
(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.
(10) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?