Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $7000

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $12040

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 = $12040 – $7000 = $5040

Thus, Simple Interest = $5040

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 × 5040}/_{7000 × 9}

= ⁵⁰⁴⁰⁰⁰/₆₃₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 9% per annum

Simple Interest = $5040 (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 = 9% of Principal

= 9% of $7000

= ⁹/₁₀₀ × 7000

= ^{9 × 7000}/₁₀₀

= ⁶³⁰⁰⁰/₁₀₀ = 630

Thus, simple Interest for 1 year = $630

Now,

∵ If the simple Interest is $630, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₃₀ years

∴ If the simple Interest is $5040, then the time = ¹/₆₃₀ × 5040 years

= ^{1 × 5040}/₆₃₀ years

= ⁵⁰⁴⁰/₆₃₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.

(3) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.

(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?

(5) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(6) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.

(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 3 years.

(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.