Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
Correct Answer
$4692
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 6%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 6
= $3450 ×6/100 × 6
= 3450 × 6 × 6/100
= 20700 × 6/100
= 124200/100
= $1242
Thus, Simple Interest = $1242
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 + $1242
= $4692
Thus, Amount to be paid = $4692 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) = 6%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 6% × 6)
= $3450 + ($3450 ×6/100 × 6)
= $3450 + (3450 × 6 × 6/100)
= $3450 + (20700 × 6/100)
= $3450 + (124200/100)
= $3450 + $1242 = $4692
Thus, Amount (A) to be paid = $4692 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3450, the simple interest in 1 year
= 6/100 × 3450
= 6 × 3450/100
= 20700/100 = $207
Thus, simple interest for 1 year = $207
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $207 × 6 = $1242
Thus, Simple Interest (SI) = $1242
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1242
= $4692
Thus, Amount to be paid = $4692 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(2) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(4) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(7) Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(9) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?