Question

Paige's investment in his savings account matured to $4,517.27 at the end of 135 days.
If the account was earning simple interest at a rate of 3.50% p.a., answer the
following
a. What was Paige's initial investment?​​

Answer 1

${\pmb{\underline{\sf{ Required \ Solution ... }}}}$

As We know that Paige's invest as:

• Amount = $4,517.27
• Time (t) = 135 days (⅓ years)
• Rate (r) = 3.50% (7/2)

If the account was earning simple interest then we've to apply the Simple Interest Formula to obtain such results as:-

$\circ {\underline{\boxed{\sf{ Interest_{(Simple)} = \dfrac{PRT}{100} }}}}$

Let the Principal be x

so, As We know that we have Amount of investment, then:-

$\colon\implies{\sf{ Interest = Amount - Principal }} \\ \\ \colon\implies{\sf{ 4,517.27-x _{(Interest)} }}$

$\circ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\sf{ 4,517.27-x = \dfrac{x \times 1 \times 7}{100 \times 3 \times 2} }} \\ \\ \\ \colon\implies{\sf{ 4,517.27-x = \dfrac{7x}{600} }} \\ \\ \\ \colon\implies{\sf{600( 4,517.27-x) = 7x }} \\ \\ \\ \colon\implies{\sf{ 2710362 - 600x = 7x }} \\ \\ \\ \colon\implies{\sf{ 2710362 = 600x+7x }} \\ \\ \\ \colon\implies{\sf{ 2710362 = 607x }} \\ \\ \\ \colon\implies{\sf{ \cancel{ \dfrac{2710362}{607} } = x }} \\ \\ \\ \colon\implies{\sf{ x = \ \ 4465.17 }}$

Hence,

Paige's initial investment was $ 4465.17.