Question:
Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
Correct Answer
$6420
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 2%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 10
= $5350 ×2/100 × 10
= 5350 × 2 × 10/100
= 10700 × 10/100
= 107000/100
= $1070
Thus, Simple Interest = $1070
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 + $1070
= $6420
Thus, Amount to be paid = $6420 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5350 + ($5350 × 2% × 10)
= $5350 + ($5350 ×2/100 × 10)
= $5350 + (5350 × 2 × 10/100)
= $5350 + (10700 × 10/100)
= $5350 + (107000/100)
= $5350 + $1070 = $6420
Thus, Amount (A) to be paid = $6420 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5350, the simple interest in 1 year
= 2/100 × 5350
= 2 × 5350/100
= 10700/100 = $107
Thus, simple interest for 1 year = $107
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $107 × 10 = $1070
Thus, Simple Interest (SI) = $1070
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $1070
= $6420
Thus, Amount to be paid = $6420 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(4) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.
(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(9) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.