Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
Correct Answer
$4485
Solution And Explanation
Solution
Given,
Principal (P) = $3450
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) = $3450 × 5% × 6
= $3450 ×5/100 × 6
= 3450 × 5 × 6/100
= 17250 × 6/100
= 103500/100
= $1035
Thus, Simple Interest = $1035
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 + $1035
= $4485
Thus, Amount to be paid = $4485 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) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 5% × 6)
= $3450 + ($3450 ×5/100 × 6)
= $3450 + (3450 × 5 × 6/100)
= $3450 + (17250 × 6/100)
= $3450 + (103500/100)
= $3450 + $1035 = $4485
Thus, Amount (A) to be paid = $4485 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 $3450, the simple interest in 1 year
= 5/100 × 3450
= 5 × 3450/100
= 17250/100 = $172.5
Thus, simple interest for 1 year = $172.5
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $172.5 × 6 = $1035
Thus, Simple Interest (SI) = $1035
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $1035
= $4485
Thus, Amount to be paid = $4485 Answer
Similar Questions
(1) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?
(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.
(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?