mcqs Math Simple Interest 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. 7431

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.

(A)  5.25
(B)  8.75
(C)  7
(D)  10.5

Correct Answer 7

Solution And Explanation

Solution

Given,

Principal (P) = $4200

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

Amount (A) = $5964

Thus, time (T) = ?

Method (1) Using Formula

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $5964 – $4200 = $1764

Thus, Simple Interest = $1764

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

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