Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
Correct Answer
$9048
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5800 ×7/100 × 8
= 5800 × 7 × 8/100
= 40600 × 8/100
= 324800/100
= $3248
Thus, Simple Interest = $3248
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 + $3248
= $9048
Thus, Amount to be paid = $9048 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5800 + ($5800 × 7% × 8)
= $5800 + ($5800 ×7/100 × 8)
= $5800 + (5800 × 7 × 8/100)
= $5800 + (40600 × 8/100)
= $5800 + (324800/100)
= $5800 + $3248 = $9048
Thus, Amount (A) to be paid = $9048 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5800, the simple interest in 1 year
= 7/100 × 5800
= 7 × 5800/100
= 40600/100 = $406
Thus, simple interest for 1 year = $406
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $406 × 8 = $3248
Thus, Simple Interest (SI) = $3248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $3248
= $9048
Thus, Amount to be paid = $9048 Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(2) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?
(7) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(8) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.