mcqs Math Simple Interest Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan. 7916

Question: Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 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) = $6200

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

Amount (A) = $9920

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9920 – $6200 = $3720

Thus, Simple Interest = $3720

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3720}/_{6200 × 6}

= ³⁷²⁰⁰⁰/₃₇₂₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $6200

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

Simple Interest = $3720 (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 $6200

= ⁶/₁₀₀ × 6200

= ^{6 × 6200}/₁₀₀

= ³⁷²⁰⁰/₁₀₀ = 372

Thus, simple Interest for 1 year = $372

Now,

∵ If the simple Interest is $372, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₂ years

∴ If the simple Interest is $3720, then the time = ¹/₃₇₂ × 3720 years

= ^{1 × 3720}/₃₇₂ years

= ³⁷²⁰/₃₇₂ = 10 years

Thus, time (T) = 10 years Answer