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) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(5) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(6) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(8) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(9) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.