Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
Correct Answer
$9880
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5200 ×10/100 × 9
= 5200 × 10 × 9/100
= 52000 × 9/100
= 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 10% × 9)
= $5200 + ($5200 ×10/100 × 9)
= $5200 + (5200 × 10 × 9/100)
= $5200 + (52000 × 9/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5200, the simple interest in 1 year
= 10/100 × 5200
= 10 × 5200/100
= 52000/100 = $520
Thus, simple interest for 1 year = $520
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $520 × 9 = $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) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.
(5) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(6) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?