Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $11410

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 = $11410 – $7000 = $4410

Thus, Simple Interest = $4410

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 × 4410}/_{7000 × 7}

= ⁴⁴¹⁰⁰⁰/₄₉₀₀₀

= 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) = $7000

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

Simple Interest = $4410 (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 $7000

= ⁷/₁₀₀ × 7000

= ^{7 × 7000}/₁₀₀

= ⁴⁹⁰⁰⁰/₁₀₀ = 490

Thus, simple Interest for 1 year = $490

Now,

∵ If the simple Interest is $490, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₀ years

∴ If the simple Interest is $4410, then the time = ¹/₄₉₀ × 4410 years

= ^{1 × 4410}/₄₉₀ years

= ⁴⁴¹⁰/₄₉₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.

(2) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.

(3) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.

(6) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.

(10) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?