Question:
Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
Correct Answer
$9945
Solution And Explanation
Solution
Given,
Principal (P) = $5850
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 7
= $5850 ×10/100 × 7
= 5850 × 10 × 7/100
= 58500 × 7/100
= 409500/100
= $4095
Thus, Simple Interest = $4095
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 + $4095
= $9945
Thus, Amount to be paid = $9945 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5850 + ($5850 × 10% × 7)
= $5850 + ($5850 ×10/100 × 7)
= $5850 + (5850 × 10 × 7/100)
= $5850 + (58500 × 7/100)
= $5850 + (409500/100)
= $5850 + $4095 = $9945
Thus, Amount (A) to be paid = $9945 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5850, the simple interest in 1 year
= 10/100 × 5850
= 10 × 5850/100
= 58500/100 = $585
Thus, simple interest for 1 year = $585
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $585 × 7 = $4095
Thus, Simple Interest (SI) = $4095
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $4095
= $9945
Thus, Amount to be paid = $9945 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(5) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?
(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?