Question:
Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
Correct Answer
$7950
Solution And Explanation
Solution
Given,
Principal (P) = $5300
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) = $5300 × 5% × 10
= $5300 ×5/100 × 10
= 5300 × 5 × 10/100
= 26500 × 10/100
= 265000/100
= $2650
Thus, Simple Interest = $2650
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 = $5300 + $2650
= $7950
Thus, Amount to be paid = $7950 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 = $5300
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5300 + ($5300 × 5% × 10)
= $5300 + ($5300 ×5/100 × 10)
= $5300 + (5300 × 5 × 10/100)
= $5300 + (26500 × 10/100)
= $5300 + (265000/100)
= $5300 + $2650 = $7950
Thus, Amount (A) to be paid = $7950 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 $5300, the simple interest in 1 year
= 5/100 × 5300
= 5 × 5300/100
= 26500/100 = $265
Thus, simple interest for 1 year = $265
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $265 × 10 = $2650
Thus, Simple Interest (SI) = $2650
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $2650
= $7950
Thus, Amount to be paid = $7950 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.
(3) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(4) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.
(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(8) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?
(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.