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) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.
(5) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(7) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(9) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.