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) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(9) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
(10) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?