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) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.
(3) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(8) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?
(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?