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) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?
(4) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?
(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.