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) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?
(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?
(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(7) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.