Simple Interest
Math MCQs

Question :    How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?

Correct Answer  $6650

Solution & Explanation

Solution

Given,

Amount (A) = $8312.5

Rate of Simple Interest (R) = 5%

Time (T) = 5 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

$8312.5 = P (1 + 5% × 5)

⇒ $8312.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8312.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8312.5 = P (1 + ²⁵/₁₀₀)

⇒ $8312.5 = P (^{100 + 25}/₁₀₀)

⇒ $8312.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8312.5

⇒ P = ^8312.5/_¹²⁵/100

⇒ P = 8312.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8312.5 × 100}/₁₂₅

⇒ P = ⁸³¹²⁵⁰/₁₂₅

⇒ P = $6650

Thus, the sum borrowed (P) = $6650 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 8312.5, then the Principal = ¹⁰⁰/₁₂₅ × 8312.5

= ^{100 × 8312.5}/₁₂₅

= ⁸³¹²⁵⁰/₁₂₅

= 6650

Thus, Principal = $6650

Thus, the sum borrowed = $6650 Answer

Similar Questions

(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.

(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?

(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.

(4) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(7) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?

(8) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

(10) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.