Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
Correct Answer
$9880
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5200 ×9/100 × 10
= 5200 × 9 × 10/100
= 46800 × 10/100
= 468000/100
= $4680
Thus, Simple Interest = $4680
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 + $4680
= $9880
Thus, Amount to be paid = $9880 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 9% × 10)
= $5200 + ($5200 ×9/100 × 10)
= $5200 + (5200 × 9 × 10/100)
= $5200 + (46800 × 10/100)
= $5200 + (468000/100)
= $5200 + $4680 = $9880
Thus, Amount (A) to be paid = $9880 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5200, the simple interest in 1 year
= 9/100 × 5200
= 9 × 5200/100
= 46800/100 = $468
Thus, simple interest for 1 year = $468
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $468 × 10 = $4680
Thus, Simple Interest (SI) = $4680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $4680
= $9880
Thus, Amount to be paid = $9880 Answer
Similar Questions
(1) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?
(3) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(7) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(8) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(9) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(10) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.