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) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(2) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(3) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
(8) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?
(9) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.