Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $7990

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 = $7990 – $4700 = $3290

Thus, Simple Interest = $3290

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 × 3290}/_{4700 × 7}

= ³²⁹⁰⁰⁰/₃₂₉₀₀

= 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) = $4700

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

Simple Interest = $3290 (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 $4700

= ⁷/₁₀₀ × 4700

= ^{7 × 4700}/₁₀₀

= ³²⁹⁰⁰/₁₀₀ = 329

Thus, simple Interest for 1 year = $329

Now,

∵ If the simple Interest is $329, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₉ years

∴ If the simple Interest is $3290, then the time = ¹/₃₂₉ × 3290 years

= ^{1 × 3290}/₃₂₉ years

= ³²⁹⁰/₃₂₉ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.

(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.

(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.

(9) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.