Question:
Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
Correct Answer
$9450
Solution And Explanation
Solution
Given,
Principal (P) = $5250
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5250 × 10% × 8
= $5250 ×10/100 × 8
= 5250 × 10 × 8/100
= 52500 × 8/100
= 420000/100
= $4200
Thus, Simple Interest = $4200
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 = $5250 + $4200
= $9450
Thus, Amount to be paid = $9450 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 = $5250
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5250 + ($5250 × 10% × 8)
= $5250 + ($5250 ×10/100 × 8)
= $5250 + (5250 × 10 × 8/100)
= $5250 + (52500 × 8/100)
= $5250 + (420000/100)
= $5250 + $4200 = $9450
Thus, Amount (A) to be paid = $9450 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5250, the simple interest in 1 year
= 10/100 × 5250
= 10 × 5250/100
= 52500/100 = $525
Thus, simple interest for 1 year = $525
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $525 × 8 = $4200
Thus, Simple Interest (SI) = $4200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5250 + $4200
= $9450
Thus, Amount to be paid = $9450 Answer
Similar Questions
(1) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?
(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(4) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?
(8) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(9) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(10) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.