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) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.

(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.

(4) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.

(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?

(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(7) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?

(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.