Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.
Correct Answer
$8362
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 6%
Time (t) = 8 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% × 8
= $5650 ×6/100 × 8
= 5650 × 6 × 8/100
= 33900 × 8/100
= 271200/100
= $2712
Thus, Simple Interest = $2712
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 + $2712
= $8362
Thus, Amount to be paid = $8362 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) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 6% × 8)
= $5650 + ($5650 ×6/100 × 8)
= $5650 + (5650 × 6 × 8/100)
= $5650 + (33900 × 8/100)
= $5650 + (271200/100)
= $5650 + $2712 = $8362
Thus, Amount (A) to be paid = $8362 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 8 years
= Simple interest for 1 year × 8
= $339 × 8 = $2712
Thus, Simple Interest (SI) = $2712
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $2712
= $8362
Thus, Amount to be paid = $8362 Answer
Similar Questions
(1) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(5) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(7) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.