Simple Interest
Math MCQs

Question :    How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?

Correct Answer  $7850

Solution & Explanation

Solution

Given,

Amount (A) = $9420

Rate of Simple Interest (R) = 4%

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

$9420 = P (1 + 4% × 5)

⇒ $9420 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9420 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9420 = P (1 + ²⁰/₁₀₀)

⇒ $9420 = P (^{100 + 20}/₁₀₀)

⇒ $9420 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9420

⇒ P = ⁹⁴²⁰/_¹²⁰/100

⇒ P = 9420 × ¹⁰⁰/₁₂₀

⇒ P = ^{9420 × 100}/₁₂₀

⇒ P = ⁹⁴²⁰⁰⁰/₁₂₀

⇒ P = $7850

Thus, the sum borrowed (P) = $7850 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 = 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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 9420, then the Principal = ¹⁰⁰/₁₂₀ × 9420

= ^{100 × 9420}/₁₂₀

= ⁹⁴²⁰⁰⁰/₁₂₀

= 7850

Thus, Principal = $7850

Thus, the sum borrowed = $7850 Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.

(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.

(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.

(7) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.

(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?

(9) Emily had to pay $5320 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?