Question

Annabella wants to make the most economical decision so she chose the 3-year car loan so that after the loan is paid off to be able to invest in a structured saving account if Anabella put $200 into a saving account each month with an annual interest rate of 3.2% interest compounded monthly how much money would she have in her account after 2 years ​

Answer 1

Explanation:

Given

• P = $200,
• t = 2 years,
• n = 12,
• 
  `\sf \: r = 3.2\% = (3.2)/(100) = 0.032`

To find

• Future value of saving

Solution

Use periodic compound formula:

`\sf \: F=P\cfrac{(1+ (r)/(n))^(nt)-1}{(r)/(n)}`

Substitute the values and calculate:

`\sf \: F=200\cfrac{(1+ (0.032)/(12))^(12 * 2)-1}{(0.032)/(12)}`

`\sf \: F=200\cfrac{( ( 12 + 0.032)/(12))^(24)-1}{(0.032)/(12)}`

`\sf \: F=200\cfrac{( {11.002 }{})^(24)-1}{0.002}`

`\sf \: F=200 * 24.7506`

`\sf \: F=4950.12rounded`

Answer 2

• Annabella will save $4950.11 after 2 years.

Explanation:

Given

• Periodic payment P = $200,
• Period t = 2 years,
• Number of compounds, monthly n = 12,
• Interest rate, r = 3.2% = 0.032.

To find

• Future value of saving, F

Solution

Use periodic compound formula:

`F=P\cfrac{(1+r/n)^(nt)-1}{r/n}`

Substitute the values and calculate:

`F=200\cfrac{(1+0.032/12)^(12*2)-1}{0.032/12} =4950.12` rounded