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 $10106 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $10106

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 = $10106 – $6200 = $3906

Thus, Simple Interest = $3906

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 × 3906}/_{6200 × 7}

= ³⁹⁰⁶⁰⁰/₄₃₄₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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 = $3906 (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 $3906, then the time = ¹/₄₃₄ × 3906 years

= ^{1 × 3906}/₄₃₄ years

= ³⁹⁰⁶/₄₃₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?

(2) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(3) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(6) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(7) 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.

(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(10) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.