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) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.