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) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(9) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(10) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.