mcqs Math Simple Interest Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan. 7978

Question: Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 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) = 8% per annum

Amount (A) = $11160

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11160 – $6200 = $4960

Thus, Simple Interest = $4960

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4960}/_{6200 × 8}

= ⁴⁹⁶⁰⁰⁰/₄₉₆₀₀

= 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) = 8% per annum

Simple Interest = $4960 (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 = 8% of Principal

= 8% of $6200

= ⁸/₁₀₀ × 6200

= ^{8 × 6200}/₁₀₀

= ⁴⁹⁶⁰⁰/₁₀₀ = 496

Thus, simple Interest for 1 year = $496

Now,

∵ If the simple Interest is $496, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₆ years

∴ If the simple Interest is $4960, then the time = ¹/₄₉₆ × 4960 years

= ^{1 × 4960}/₄₉₆ years

= ⁴⁹⁶⁰/₄₉₆ = 10 years

Thus, time (T) = 10 years Answer