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 $11900 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $11900

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 = $11900 – $7000 = $4900

Thus, Simple Interest = $4900

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 × 4900}/_{7000 × 7}

= ⁴⁹⁰⁰⁰⁰/₄₉₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $4900 (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 $4900, then the time = ¹/₄₉₀ × 4900 years

= ^{1 × 4900}/₄₉₀ years

= ⁴⁹⁰⁰/₄₉₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.

(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.

(5) 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.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.

(7) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?

(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.

(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.