Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
Correct Answer
$6180
Solution And Explanation
Solution
Given,
Principal (P) = $5150
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) = $5150 × 2% × 10
= $5150 ×2/100 × 10
= 5150 × 2 × 10/100
= 10300 × 10/100
= 103000/100
= $1030
Thus, Simple Interest = $1030
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 + $1030
= $6180
Thus, Amount to be paid = $6180 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) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 2% × 10)
= $5150 + ($5150 ×2/100 × 10)
= $5150 + (5150 × 2 × 10/100)
= $5150 + (10300 × 10/100)
= $5150 + (103000/100)
= $5150 + $1030 = $6180
Thus, Amount (A) to be paid = $6180 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 $5150, the simple interest in 1 year
= 2/100 × 5150
= 2 × 5150/100
= 10300/100 = $103
Thus, simple interest for 1 year = $103
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $103 × 10 = $1030
Thus, Simple Interest (SI) = $1030
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1030
= $6180
Thus, Amount to be paid = $6180 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?
(4) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(6) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(9) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(10) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $7752 to clear the loan, then find the time period of the loan.