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 $6880 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $6880

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 = $6880 – $4300 = $2580

Thus, Simple Interest = $2580

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 × 2580}/_{4300 × 6}

= ²⁵⁸⁰⁰⁰/₂₅₈₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $2580 (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 $2580, then the time = ¹/₂₅₈ × 2580 years

= ^{1 × 2580}/₂₅₈ years

= ²⁵⁸⁰/₂₅₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.

(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(4) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.

(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.

(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.