Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $10200

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 = $10200 – $6000 = $4200

Thus, Simple Interest = $4200

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 × 4200}/_{6000 × 7}

= ⁴²⁰⁰⁰⁰/₄₂₀₀₀

= 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) = $6000

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $4200 (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 = 7% of Principal

= 7% of $6000

= ⁷/₁₀₀ × 6000

= ^{7 × 6000}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $4200, then the time = ¹/₄₂₀ × 4200 years

= ^{1 × 4200}/₄₂₀ years

= ⁴²⁰⁰/₄₂₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.

(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?

(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.