Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $7000

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $11200

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 = $11200 – $7000 = $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}/_{7000 × 10}

= ⁴²⁰⁰⁰⁰/₇₀₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $7000

Rate of Simple Interest (R) = 10% 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 = 10% of Principal

= 10% of $7000

= ¹⁰/₁₀₀ × 7000

= ^{10 × 7000}/₁₀₀

= ⁷⁰⁰⁰⁰/₁₀₀ = 700

Thus, simple Interest for 1 year = $700

Now,

∵ If the simple Interest is $700, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₇₀₀ years

∴ If the simple Interest is $4200, then the time = ¹/₇₀₀ × 4200 years

= ^{1 × 4200}/₇₀₀ years

= ⁴²⁰⁰/₇₀₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.

(6) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?

(7) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(8) If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(10) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.