Question:
Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
Correct Answer
$9040
Solution And Explanation
Solution
Given,
Principal (P) = $5650
Rate of Simple Interest (SI) = 6%
Time (t) = 10 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) = $5650 × 6% × 10
= $5650 ×6/100 × 10
= 5650 × 6 × 10/100
= 33900 × 10/100
= 339000/100
= $3390
Thus, Simple Interest = $3390
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 = $5650 + $3390
= $9040
Thus, Amount to be paid = $9040 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 = $5650
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5650 + ($5650 × 6% × 10)
= $5650 + ($5650 ×6/100 × 10)
= $5650 + (5650 × 6 × 10/100)
= $5650 + (33900 × 10/100)
= $5650 + (339000/100)
= $5650 + $3390 = $9040
Thus, Amount (A) to be paid = $9040 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 $5650, the simple interest in 1 year
= 6/100 × 5650
= 6 × 5650/100
= 33900/100 = $339
Thus, simple interest for 1 year = $339
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $339 × 10 = $3390
Thus, Simple Interest (SI) = $3390
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5650 + $3390
= $9040
Thus, Amount to be paid = $9040 Answer
Similar Questions
(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?
(6) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?
(8) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(10) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.