Question:
What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
Correct Answer
$4810
Solution And Explanation
Solution
Given,
Principal (P) = $3700
Rate of Simple Interest (SI) = 5%
Time (t) = 6 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) = $3700 × 5% × 6
= $3700 ×5/100 × 6
= 3700 × 5 × 6/100
= 18500 × 6/100
= 111000/100
= $1110
Thus, Simple Interest = $1110
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 = $3700 + $1110
= $4810
Thus, Amount to be paid = $4810 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 = $3700
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3700 + ($3700 × 5% × 6)
= $3700 + ($3700 ×5/100 × 6)
= $3700 + (3700 × 5 × 6/100)
= $3700 + (18500 × 6/100)
= $3700 + (111000/100)
= $3700 + $1110 = $4810
Thus, Amount (A) to be paid = $4810 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 $3700, the simple interest in 1 year
= 5/100 × 3700
= 5 × 3700/100
= 18500/100 = $185
Thus, simple interest for 1 year = $185
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $185 × 6 = $1110
Thus, Simple Interest (SI) = $1110
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3700 + $1110
= $4810
Thus, Amount to be paid = $4810 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(2) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(4) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(5) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(6) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(10) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.