Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
Correct Answer
$8023
Solution And Explanation
Solution
Given,
Principal (P) = $5650
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) = $5650 × 6% × 7
= $5650 ×6/100 × 7
= 5650 × 6 × 7/100
= 33900 × 7/100
= 237300/100
= $2373
Thus, Simple Interest = $2373
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 = $5650 + $2373
= $8023
Thus, Amount to be paid = $8023 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 = $5650
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5650 + ($5650 × 6% × 7)
= $5650 + ($5650 ×6/100 × 7)
= $5650 + (5650 × 6 × 7/100)
= $5650 + (33900 × 7/100)
= $5650 + (237300/100)
= $5650 + $2373 = $8023
Thus, Amount (A) to be paid = $8023 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 $5650, the simple interest in 1 year
= 6/100 × 5650
= 6 × 5650/100
= 33900/100 = $339
Thus, simple interest for 1 year = $339
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $339 × 7 = $2373
Thus, Simple Interest (SI) = $2373
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2373
= $8023
Thus, Amount to be paid = $8023 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(4) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(6) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?