Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
Correct Answer
$9512
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 8%
Time (t) = 8 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) = $5800 × 8% × 8
= $5800 ×8/100 × 8
= 5800 × 8 × 8/100
= 46400 × 8/100
= 371200/100
= $3712
Thus, Simple Interest = $3712
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 + $3712
= $9512
Thus, Amount to be paid = $9512 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 8% × 8)
= $5800 + ($5800 ×8/100 × 8)
= $5800 + (5800 × 8 × 8/100)
= $5800 + (46400 × 8/100)
= $5800 + (371200/100)
= $5800 + $3712 = $9512
Thus, Amount (A) to be paid = $9512 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 $5800, the simple interest in 1 year
= 8/100 × 5800
= 8 × 5800/100
= 46400/100 = $464
Thus, simple interest for 1 year = $464
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $464 × 8 = $3712
Thus, Simple Interest (SI) = $3712
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $3712
= $9512
Thus, Amount to be paid = $9512 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(2) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.
(4) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.
(7) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(8) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.