Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6622

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 = $6622 – $4300 = $2322

Thus, Simple Interest = $2322

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 × 2322}/_{4300 × 6}

= ²³²²⁰⁰/₂₅₈₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4300

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2322 (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 = 6% of Principal

= 6% of $4300

= ⁶/₁₀₀ × 4300

= ^{6 × 4300}/₁₀₀

= ²⁵⁸⁰⁰/₁₀₀ = 258

Thus, simple Interest for 1 year = $258

Now,

∵ If the simple Interest is $258, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₅₈ years

∴ If the simple Interest is $2322, then the time = ¹/₂₅₈ × 2322 years

= ^{1 × 2322}/₂₅₈ years

= ²³²²/₂₅₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.

(2) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.

(4) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?

(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?

(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.

(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.