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 $10780 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) = 9% per annum

Amount (A) = $10780

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 = $10780 – $7000 = $3780

Thus, Simple Interest = $3780

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 × 3780}/_{7000 × 9}

= ³⁷⁸⁰⁰⁰/₆₃₀₀₀

= 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) = 9% per annum

Simple Interest = $3780 (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 $3780, then the time = ¹/₆₃₀ × 3780 years

= ^{1 × 3780}/₆₃₀ years

= ³⁷⁸⁰/₆₃₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(2) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.

(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?

(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?

(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(9) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.

(10) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.