Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
Correct Answer
$9976
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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) = $5800 × 9% × 8
= $5800 ×9/100 × 8
= 5800 × 9 × 8/100
= 52200 × 8/100
= 417600/100
= $4176
Thus, Simple Interest = $4176
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 = $5800 + $4176
= $9976
Thus, Amount to be paid = $9976 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 = $5800
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 9% × 8)
= $5800 + ($5800 ×9/100 × 8)
= $5800 + (5800 × 9 × 8/100)
= $5800 + (52200 × 8/100)
= $5800 + (417600/100)
= $5800 + $4176 = $9976
Thus, Amount (A) to be paid = $9976 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5800, the simple interest in 1 year
= 9/100 × 5800
= 9 × 5800/100
= 52200/100 = $522
Thus, simple interest for 1 year = $522
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $522 × 8 = $4176
Thus, Simple Interest (SI) = $4176
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $4176
= $9976
Thus, Amount to be paid = $9976 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(3) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(4) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?
(5) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(9) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.