Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
Correct Answer
$9095
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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% × 10
= $5350 ×7/100 × 10
= 5350 × 7 × 10/100
= 37450 × 10/100
= 374500/100
= $3745
Thus, Simple Interest = $3745
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 + $3745
= $9095
Thus, Amount to be paid = $9095 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) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 7% × 10)
= $5350 + ($5350 ×7/100 × 10)
= $5350 + (5350 × 7 × 10/100)
= $5350 + (37450 × 10/100)
= $5350 + (374500/100)
= $5350 + $3745 = $9095
Thus, Amount (A) to be paid = $9095 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 10 years
= Simple interest for 1 year × 10
= $374.5 × 10 = $3745
Thus, Simple Interest (SI) = $3745
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $3745
= $9095
Thus, Amount to be paid = $9095 Answer
Similar Questions
(1) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(4) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(5) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?
(6) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(9) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.