Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
Correct Answer
$6962
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5900 × 2% × 9
= $5900 ×2/100 × 9
= 5900 × 2 × 9/100
= 11800 × 9/100
= 106200/100
= $1062
Thus, Simple Interest = $1062
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 = $5900 + $1062
= $6962
Thus, Amount to be paid = $6962 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 = $5900
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 2% × 9)
= $5900 + ($5900 ×2/100 × 9)
= $5900 + (5900 × 2 × 9/100)
= $5900 + (11800 × 9/100)
= $5900 + (106200/100)
= $5900 + $1062 = $6962
Thus, Amount (A) to be paid = $6962 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5900, the simple interest in 1 year
= 2/100 × 5900
= 2 × 5900/100
= 11800/100 = $118
Thus, simple interest for 1 year = $118
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $118 × 9 = $1062
Thus, Simple Interest (SI) = $1062
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $1062
= $6962
Thus, Amount to be paid = $6962 Answer
Similar Questions
(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(6) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(7) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.