Question:
What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
Correct Answer
$4140
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 4%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $3450 × 4% × 5
= $3450 ×4/100 × 5
= 3450 × 4 × 5/100
= 13800 × 5/100
= 69000/100
= $690
Thus, Simple Interest = $690
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 = $3450 + $690
= $4140
Thus, Amount to be paid = $4140 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 = $3450
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 5 years
Thus, Amount (A)
= $3450 + ($3450 × 4% × 5)
= $3450 + ($3450 ×4/100 × 5)
= $3450 + (3450 × 4 × 5/100)
= $3450 + (13800 × 5/100)
= $3450 + (69000/100)
= $3450 + $690 = $4140
Thus, Amount (A) to be paid = $4140 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3450, the simple interest in 1 year
= 4/100 × 3450
= 4 × 3450/100
= 13800/100 = $138
Thus, simple interest for 1 year = $138
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $138 × 5 = $690
Thus, Simple Interest (SI) = $690
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $690
= $4140
Thus, Amount to be paid = $4140 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.
(6) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(8) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(10) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?