Simple Interest
Math MCQs

Question :    Kimberly had to pay $5208 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  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $5208

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

$5208 = P (1 + 4% × 3)

⇒ $5208 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5208 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5208 = P (1 + ¹²/₁₀₀)

⇒ $5208 = P (^{100 + 12}/₁₀₀)

⇒ $5208 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5208

⇒ P = ⁵²⁰⁸/_¹¹²/100

⇒ P = 5208 × ¹⁰⁰/₁₁₂

⇒ P = ^{5208 × 100}/₁₁₂

⇒ P = ⁵²⁰⁸⁰⁰/₁₁₂

⇒ P = $4650

Thus, the sum borrowed (P) = $4650 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 5208, then the Principal = ¹⁰⁰/₁₁₂ × 5208

= ^{100 × 5208}/₁₁₂

= ⁵²⁰⁸⁰⁰/₁₁₂

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(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) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?

(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 6% simple interest?

(6) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?

(8) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?