Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
Correct Answer
$8034
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5150 × 8% × 7
= $5150 ×8/100 × 7
= 5150 × 8 × 7/100
= 41200 × 7/100
= 288400/100
= $2884
Thus, Simple Interest = $2884
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 = $5150 + $2884
= $8034
Thus, Amount to be paid = $8034 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 = $5150
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 8% × 7)
= $5150 + ($5150 ×8/100 × 7)
= $5150 + (5150 × 8 × 7/100)
= $5150 + (41200 × 7/100)
= $5150 + (288400/100)
= $5150 + $2884 = $8034
Thus, Amount (A) to be paid = $8034 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5150, the simple interest in 1 year
= 8/100 × 5150
= 8 × 5150/100
= 41200/100 = $412
Thus, simple interest for 1 year = $412
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $412 × 7 = $2884
Thus, Simple Interest (SI) = $2884
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2884
= $8034
Thus, Amount to be paid = $8034 Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(6) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?