Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $5964

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 = $5964 – $4200 = $1764

Thus, Simple Interest = $1764

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 × 1764}/_{4200 × 6}

= ¹⁷⁶⁴⁰⁰/₂₅₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 6% per annum

Simple Interest = $1764 (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 = 6% of Principal

= 6% of $4200

= ⁶/₁₀₀ × 4200

= ^{6 × 4200}/₁₀₀

= ²⁵²⁰⁰/₁₀₀ = 252

Thus, simple Interest for 1 year = $252

Now,

∵ If the simple Interest is $252, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₅₂ years

∴ If the simple Interest is $1764, then the time = ¹/₂₅₂ × 1764 years

= ^{1 × 1764}/₂₅₂ years

= ¹⁷⁶⁴/₂₅₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?

(4) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.

(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.

(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.