Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
Correct Answer
$6240
Solution And Explanation
Solution
Given,
Principal (P) = $5200
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) = $5200 × 2% × 10
= $5200 ×2/100 × 10
= 5200 × 2 × 10/100
= 10400 × 10/100
= 104000/100
= $1040
Thus, Simple Interest = $1040
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 = $5200 + $1040
= $6240
Thus, Amount to be paid = $6240 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 = $5200
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 2% × 10)
= $5200 + ($5200 ×2/100 × 10)
= $5200 + (5200 × 2 × 10/100)
= $5200 + (10400 × 10/100)
= $5200 + (104000/100)
= $5200 + $1040 = $6240
Thus, Amount (A) to be paid = $6240 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 $5200, the simple interest in 1 year
= 2/100 × 5200
= 2 × 5200/100
= 10400/100 = $104
Thus, simple interest for 1 year = $104
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $104 × 10 = $1040
Thus, Simple Interest (SI) = $1040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1040
= $6240
Thus, Amount to be paid = $6240 Answer
Similar Questions
(1) How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(4) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.