Simple Interest
Math MCQs

Question :    Lisa had to pay $4536 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  $4050

Solution & Explanation

Solution

Given,

Amount (A) = $4536

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

$4536 = P (1 + 4% × 3)

⇒ $4536 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4536 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4536 = P (1 + ¹²/₁₀₀)

⇒ $4536 = P (^{100 + 12}/₁₀₀)

⇒ $4536 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4536

⇒ P = ⁴⁵³⁶/_¹¹²/100

⇒ P = 4536 × ¹⁰⁰/₁₁₂

⇒ P = ^{4536 × 100}/₁₁₂

⇒ P = ⁴⁵³⁶⁰⁰/₁₁₂

⇒ P = $4050

Thus, the sum borrowed (P) = $4050 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 4536, then the Principal = ¹⁰⁰/₁₁₂ × 4536

= ^{100 × 4536}/₁₁₂

= ⁴⁵³⁶⁰⁰/₁₁₂

= 4050

Thus, Principal = $4050

Thus, the sum borrowed = $4050 Answer

Similar Questions

(1) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?

(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?

(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(5) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?

(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?

(9) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.

(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.