Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7602

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 = $7602 – $4200 = $3402

Thus, Simple Interest = $3402

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 × 3402}/_{4200 × 9}

= ³⁴⁰²⁰⁰/₃₇₈₀₀

= 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) = $4200

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3402 (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 $4200

= ⁹/₁₀₀ × 4200

= ^{9 × 4200}/₁₀₀

= ³⁷⁸⁰⁰/₁₀₀ = 378

Thus, simple Interest for 1 year = $378

Now,

∵ If the simple Interest is $378, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₈ years

∴ If the simple Interest is $3402, then the time = ¹/₃₇₈ × 3402 years

= ^{1 × 3402}/₃₇₈ years

= ³⁴⁰²/₃₇₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?

(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?

(6) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.

(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?

(9) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(10) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?