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) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(2) How much loan did Lisa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7260 to clear it?
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(4) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?
(6) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?