mcqs Math Simple Interest Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan. 7906

Question: Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(A)  7.5
(B)  12.5
(C)  10
(D)  15

Correct Answer 10

Solution And Explanation

Solution

Given,

Principal (P) = $5200

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

Amount (A) = $8320

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8320 – $5200 = $3120

Thus, Simple Interest = $3120

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3120}/_{5200 × 6}

= ³¹²⁰⁰⁰/₃₁₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $5200

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

Simple Interest = $3120 (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 $5200

= ⁶/₁₀₀ × 5200

= ^{6 × 5200}/₁₀₀

= ³¹²⁰⁰/₁₀₀ = 312

Thus, simple Interest for 1 year = $312

Now,

∵ If the simple Interest is $312, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₂ years

∴ If the simple Interest is $3120, then the time = ¹/₃₁₂ × 3120 years

= ^{1 × 3120}/₃₁₂ years

= ³¹²⁰/₃₁₂ = 10 years

Thus, time (T) = 10 years Answer