Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
Correct Answer
$10148
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5900 × 8% × 9
= $5900 ×8/100 × 9
= 5900 × 8 × 9/100
= 47200 × 9/100
= 424800/100
= $4248
Thus, Simple Interest = $4248
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 = $5900 + $4248
= $10148
Thus, Amount to be paid = $10148 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 = $5900
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 8% × 9)
= $5900 + ($5900 ×8/100 × 9)
= $5900 + (5900 × 8 × 9/100)
= $5900 + (47200 × 9/100)
= $5900 + (424800/100)
= $5900 + $4248 = $10148
Thus, Amount (A) to be paid = $10148 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5900, the simple interest in 1 year
= 8/100 × 5900
= 8 × 5900/100
= 47200/100 = $472
Thus, simple interest for 1 year = $472
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $472 × 9 = $4248
Thus, Simple Interest (SI) = $4248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4248
= $10148
Thus, Amount to be paid = $10148 Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% 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 $7987 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?
(7) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?
(10) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.