Simple Interest
Math MCQs

Question :    How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?

Correct Answer  $5850

Solution & Explanation

Solution

Given,

Amount (A) = $7020

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

$7020 = P (1 + 4% × 5)

⇒ $7020 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7020 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7020 = P (1 + ²⁰/₁₀₀)

⇒ $7020 = P (^{100 + 20}/₁₀₀)

⇒ $7020 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7020

⇒ P = ⁷⁰²⁰/_¹²⁰/100

⇒ P = 7020 × ¹⁰⁰/₁₂₀

⇒ P = ^{7020 × 100}/₁₂₀

⇒ P = ⁷⁰²⁰⁰⁰/₁₂₀

⇒ P = $5850

Thus, the sum borrowed (P) = $5850 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 7020, then the Principal = ¹⁰⁰/₁₂₀ × 7020

= ^{100 × 7020}/₁₂₀

= ⁷⁰²⁰⁰⁰/₁₂₀

= 5850

Thus, Principal = $5850

Thus, the sum borrowed = $5850 Answer

Similar Questions

(1) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?

(6) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.

(10) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?