Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $6720

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 = $6720 – $4200 = $2520

Thus, Simple Interest = $2520

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 × 2520}/_{4200 × 10}

= ²⁵²⁰⁰⁰/₄₂₀₀₀

= 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) = $4200

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $2520 (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 = 10% of Principal

= 10% of $4200

= ¹⁰/₁₀₀ × 4200

= ^{10 × 4200}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $2520, then the time = ¹/₄₂₀ × 2520 years

= ^{1 × 2520}/₄₂₀ years

= ²⁵²⁰/₄₂₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.

(2) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.

(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(9) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?

(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.