Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
Correct Answer
$8008
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5200 ×6/100 × 9
= 5200 × 6 × 9/100
= 31200 × 9/100
= 280800/100
= $2808
Thus, Simple Interest = $2808
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 + $2808
= $8008
Thus, Amount to be paid = $8008 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 6% × 9)
= $5200 + ($5200 ×6/100 × 9)
= $5200 + (5200 × 6 × 9/100)
= $5200 + (31200 × 9/100)
= $5200 + (280800/100)
= $5200 + $2808 = $8008
Thus, Amount (A) to be paid = $8008 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5200, the simple interest in 1 year
= 6/100 × 5200
= 6 × 5200/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $312 × 9 = $2808
Thus, Simple Interest (SI) = $2808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2808
= $8008
Thus, Amount to be paid = $8008 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 5% simple interest?
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.
(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
(7) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(8) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.