Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
Correct Answer
$8307
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 6%
Time (t) = 7 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% × 7
= $5850 ×6/100 × 7
= 5850 × 6 × 7/100
= 35100 × 7/100
= 245700/100
= $2457
Thus, Simple Interest = $2457
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 + $2457
= $8307
Thus, Amount to be paid = $8307 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) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 6% × 7)
= $5850 + ($5850 ×6/100 × 7)
= $5850 + (5850 × 6 × 7/100)
= $5850 + (35100 × 7/100)
= $5850 + (245700/100)
= $5850 + $2457 = $8307
Thus, Amount (A) to be paid = $8307 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 7 years
= Simple interest for 1 year × 7
= $351 × 7 = $2457
Thus, Simple Interest (SI) = $2457
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $2457
= $8307
Thus, Amount to be paid = $8307 Answer
Similar Questions
(1) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(4) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(10) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.