Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7912

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7912 – $4600 = $3312

Thus, Simple Interest = $3312

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3312}/_{4600 × 9}

= ³³¹²⁰⁰/₄₁₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $4600

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3312 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 9% of Principal

= 9% of $4600

= ⁹/₁₀₀ × 4600

= ^{9 × 4600}/₁₀₀

= ⁴¹⁴⁰⁰/₁₀₀ = 414

Thus, simple Interest for 1 year = $414

Now,

∵ If the simple Interest is $414, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₄ years

∴ If the simple Interest is $3312, then the time = ¹/₄₁₄ × 3312 years

= ^{1 × 3312}/₄₁₄ years

= ³³¹²/₄₁₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(3) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(4) If Barbara paid $4118 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(6) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.

(9) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.