Simple Interest
Math MCQs

Question :    How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?

Correct Answer  $6850

Solution & Explanation

Solution

Given,

Amount (A) = $8220

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

$8220 = P (1 + 4% × 5)

⇒ $8220 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8220 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8220 = P (1 + ²⁰/₁₀₀)

⇒ $8220 = P (^{100 + 20}/₁₀₀)

⇒ $8220 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8220

⇒ P = ⁸²²⁰/_¹²⁰/100

⇒ P = 8220 × ¹⁰⁰/₁₂₀

⇒ P = ^{8220 × 100}/₁₂₀

⇒ P = ⁸²²⁰⁰⁰/₁₂₀

⇒ P = $6850

Thus, the sum borrowed (P) = $6850 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 8220, then the Principal = ¹⁰⁰/₁₂₀ × 8220

= ^{100 × 8220}/₁₂₀

= ⁸²²⁰⁰⁰/₁₂₀

= 6850

Thus, Principal = $6850

Thus, the sum borrowed = $6850 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

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

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.

(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.

(7) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(8) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.

(9) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 8% simple interest?