Question:
Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
Correct Answer
$8850
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5900 ×5/100 × 10
= 5900 × 5 × 10/100
= 29500 × 10/100
= 295000/100
= $2950
Thus, Simple Interest = $2950
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 + $2950
= $8850
Thus, Amount to be paid = $8850 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5900 + ($5900 × 5% × 10)
= $5900 + ($5900 ×5/100 × 10)
= $5900 + (5900 × 5 × 10/100)
= $5900 + (29500 × 10/100)
= $5900 + (295000/100)
= $5900 + $2950 = $8850
Thus, Amount (A) to be paid = $8850 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5900, the simple interest in 1 year
= 5/100 × 5900
= 5 × 5900/100
= 29500/100 = $295
Thus, simple interest for 1 year = $295
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $295 × 10 = $2950
Thus, Simple Interest (SI) = $2950
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2950
= $8850
Thus, Amount to be paid = $8850 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(8) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10168 to clear the loan, then find the time period of the loan.
(10) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.