Question:
Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.
Correct Answer
$7006
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5650 ×3/100 × 8
= 5650 × 3 × 8/100
= 16950 × 8/100
= 135600/100
= $1356
Thus, Simple Interest = $1356
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 + $1356
= $7006
Thus, Amount to be paid = $7006 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5650 + ($5650 × 3% × 8)
= $5650 + ($5650 ×3/100 × 8)
= $5650 + (5650 × 3 × 8/100)
= $5650 + (16950 × 8/100)
= $5650 + (135600/100)
= $5650 + $1356 = $7006
Thus, Amount (A) to be paid = $7006 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5650, the simple interest in 1 year
= 3/100 × 5650
= 3 × 5650/100
= 16950/100 = $169.5
Thus, simple interest for 1 year = $169.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $169.5 × 8 = $1356
Thus, Simple Interest (SI) = $1356
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $1356
= $7006
Thus, Amount to be paid = $7006 Answer
Similar Questions
(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?
(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?
(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.