Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
Correct Answer
$8346
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5350 × 7% × 8
= $5350 ×7/100 × 8
= 5350 × 7 × 8/100
= 37450 × 8/100
= 299600/100
= $2996
Thus, Simple Interest = $2996
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 = $5350 + $2996
= $8346
Thus, Amount to be paid = $8346 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 = $5350
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 7% × 8)
= $5350 + ($5350 ×7/100 × 8)
= $5350 + (5350 × 7 × 8/100)
= $5350 + (37450 × 8/100)
= $5350 + (299600/100)
= $5350 + $2996 = $8346
Thus, Amount (A) to be paid = $8346 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5350, the simple interest in 1 year
= 7/100 × 5350
= 7 × 5350/100
= 37450/100 = $374.5
Thus, simple interest for 1 year = $374.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $374.5 × 8 = $2996
Thus, Simple Interest (SI) = $2996
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $2996
= $8346
Thus, Amount to be paid = $8346 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?
(3) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(4) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(8) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?
(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.