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 $12670 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) = 9% per annum

Amount (A) = $12670

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 = $12670 – $7000 = $5670

Thus, Simple Interest = $5670

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 × 5670}/_{7000 × 9}

= ⁵⁶⁷⁰⁰⁰/₆₃₀₀₀

= 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) = 9% per annum

Simple Interest = $5670 (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 $5670, then the time = ¹/₆₃₀ × 5670 years

= ^{1 × 5670}/₆₃₀ years

= ⁵⁶⁷⁰/₆₃₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) 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.

(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 5% simple interest?

(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.

(4) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

(5) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.

(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.

(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?