Question

Sarah invests $8200 in a new savings account which earns 5.8% annual interest, compounded semi-annually.

what will be the value of her investment after four years?

Answer 1

$10,307.11

Explanation:

Compound Interest Formula

`\large \text{$ \sf A=P\left(1+(r)/(n)\right)^(nt) $}`

where:

• A = Final amount.
• P = Principal amount.
• r = Interest rate (in decimal form).
• n = Number of times interest is applied per year.
• t = Time (in years).

Given:

• P = $8,200
• r = 5.8% = 0.058
• n = 2 (semi-annually)
• t = 4 years

Substitute the given values into the formula and solve for A:

`\implies \sf A=8200\left(1+(0.058)/(2)\right)^(2 * 4)`

`\implies \sf A=8200\left(1+0.029\right)^(8)`

`\implies \sf A=8200\left(1.029\right)^(8)`

`\implies \sf A=8200\left(1.25696445...\right)`

`\implies \sf A=10307.10856...`

Therefore, the value of Sarah's investment after four years is $10,307.11 (nearest cent).

Answer 2

• The value after 4 years is $10307.11

--------------------------------

Given

• Invested amount P = $8200,
• Interest rate r = 5.8% = 0.058,
• Compound number n = 2,
• Time t = 4 years.

Find the future amount

• 
  `A = P(1+r/n)^(nt)`
• 
  `A = 8200(1+0.058/2)^(2*4)=8200*1.029^8=10307.11`