Simple Interest
MCQs Math


Question:     Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.


Correct Answer  $3650

Solution And Explanation

Solution

Given,

Amount (A) = $4088

Rate of Simple Interest (R) = 4%

Time (T) = 3 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$4088 = P (1 + 4% × 3)

⇒ $4088 = P (1 + 4/100 × 3)

⇒ $4088 = P (1 + 4 × 3/100)

⇒ $4088 = P (1 + 12/100)

⇒ $4088 = P (100 + 12/100)

⇒ $4088 = P × 112/100

⇒ P × 112/100 = $4088

⇒ P = 4088/112/100

⇒ P = 4088 × 100/112

⇒ P = 4088 × 100/112

⇒ P = 408800/112

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/112

∴ If the Amount is 4088, then the Principal = 100/112 × 4088

= 100 × 4088/112

= 408800/112

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer


Similar Questions

(1) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?

(3) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?

(4) If Kimberly paid $5208 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.

(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?

(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?


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