Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
Correct Answer
$8658
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5850 × 6% × 8
= $5850 ×6/100 × 8
= 5850 × 6 × 8/100
= 35100 × 8/100
= 280800/100
= $2808
Thus, Simple Interest = $2808
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 = $5850 + $2808
= $8658
Thus, Amount to be paid = $8658 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 = $5850
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5850 + ($5850 × 6% × 8)
= $5850 + ($5850 ×6/100 × 8)
= $5850 + (5850 × 6 × 8/100)
= $5850 + (35100 × 8/100)
= $5850 + (280800/100)
= $5850 + $2808 = $8658
Thus, Amount (A) to be paid = $8658 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5850, the simple interest in 1 year
= 6/100 × 5850
= 6 × 5850/100
= 35100/100 = $351
Thus, simple interest for 1 year = $351
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $351 × 8 = $2808
Thus, Simple Interest (SI) = $2808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $2808
= $8658
Thus, Amount to be paid = $8658 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(2) 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.
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(5) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(6) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(9) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.