Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6200

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9672

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 = $9672 – $6200 = $3472

Thus, Simple Interest = $3472

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 × 3472}/_{6200 × 7}

= ³⁴⁷²⁰⁰/₄₃₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6200

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3472 (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 = 7% of Principal

= 7% of $6200

= ⁷/₁₀₀ × 6200

= ^{7 × 6200}/₁₀₀

= ⁴³⁴⁰⁰/₁₀₀ = 434

Thus, simple Interest for 1 year = $434

Now,

∵ If the simple Interest is $434, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₄ years

∴ If the simple Interest is $3472, then the time = ¹/₄₃₄ × 3472 years

= ^{1 × 3472}/₄₃₄ years

= ³⁴⁷²/₄₃₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?

(5) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.

(6) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(7) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(9) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?