Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
Correct Answer
$9202
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 8%
Time (t) = 9 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) = $5350 × 8% × 9
= $5350 ×8/100 × 9
= 5350 × 8 × 9/100
= 42800 × 9/100
= 385200/100
= $3852
Thus, Simple Interest = $3852
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 + $3852
= $9202
Thus, Amount to be paid = $9202 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 8% × 9)
= $5350 + ($5350 ×8/100 × 9)
= $5350 + (5350 × 8 × 9/100)
= $5350 + (42800 × 9/100)
= $5350 + (385200/100)
= $5350 + $3852 = $9202
Thus, Amount (A) to be paid = $9202 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 $5350, the simple interest in 1 year
= 8/100 × 5350
= 8 × 5350/100
= 42800/100 = $428
Thus, simple interest for 1 year = $428
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $428 × 9 = $3852
Thus, Simple Interest (SI) = $3852
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $3852
= $9202
Thus, Amount to be paid = $9202 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(2) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(8) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.