Question:
What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
Correct Answer
$4602
Solution And Explanation
Solution
Given,
Principal (P) = $3900
Rate of Simple Interest (SI) = 3%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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) = $3900 × 3% × 6
= $3900 ×3/100 × 6
= 3900 × 3 × 6/100
= 11700 × 6/100
= 70200/100
= $702
Thus, Simple Interest = $702
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 = $3900 + $702
= $4602
Thus, Amount to be paid = $4602 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 = $3900
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 6 years
Thus, Amount (A)
= $3900 + ($3900 × 3% × 6)
= $3900 + ($3900 ×3/100 × 6)
= $3900 + (3900 × 3 × 6/100)
= $3900 + (11700 × 6/100)
= $3900 + (70200/100)
= $3900 + $702 = $4602
Thus, Amount (A) to be paid = $4602 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3900, the simple interest in 1 year
= 3/100 × 3900
= 3 × 3900/100
= 11700/100 = $117
Thus, simple interest for 1 year = $117
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $117 × 6 = $702
Thus, Simple Interest (SI) = $702
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3900 + $702
= $4602
Thus, Amount to be paid = $4602 Answer
Similar Questions
(1) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(3) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?
(4) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(6) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 4 years.