Question:
Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
Correct Answer
$7020
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 2% × 10
= $5850 ×2/100 × 10
= 5850 × 2 × 10/100
= 11700 × 10/100
= 117000/100
= $1170
Thus, Simple Interest = $1170
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 = $5850 + $1170
= $7020
Thus, Amount to be paid = $7020 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 = $5850
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5850 + ($5850 × 2% × 10)
= $5850 + ($5850 ×2/100 × 10)
= $5850 + (5850 × 2 × 10/100)
= $5850 + (11700 × 10/100)
= $5850 + (117000/100)
= $5850 + $1170 = $7020
Thus, Amount (A) to be paid = $7020 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 $5850, the simple interest in 1 year
= 2/100 × 5850
= 2 × 5850/100
= 11700/100 = $117
Thus, simple interest for 1 year = $117
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $117 × 10 = $1170
Thus, Simple Interest (SI) = $1170
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $1170
= $7020
Thus, Amount to be paid = $7020 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(7) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(10) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?