Question

Find the future value and interest earned if $8,806.54 is invested for 7 years at 4% compounded (a) semiannually and (b) continuously.(a) The future value when interest is compounded semi-annually is approximately?(Type an integer or decimal rounded to the nearest hundredth as needed.)

Answer 1

Given:

a.) Find the future value and interest earned if $8,806.54

b.) Invested for 7 years at 4% compounded semi-annually

We will be using the following formula:

`\text{ FV = P\lparen1 + }\frac{\text{ r }}{\text{ n }})^{\text{nt}}`

Where,

FV = Future value

P = Principal amount/Amount invested = $8,806.54

r = Interest rate (in decimal) = 4% = 4/100 = 0.04

n = Number of times interest is compounded = semi-annually = 2

t = Time (in years) = 7

We get,

`\text{ FV = \lparen8,806.54\rparen\lparen1 + }(0.04)/(2))^((2)(7))\text{ = \lparen8,806.54\rparen\lparen1 + 0.02\rparen}^(14)`
`\text{ FV = \lparen8,806.54\rparen\lparen1.02\rparen}^(14)`
`\text{ FV = 11,620.04250606371}`
`\text{ FV }\approx\text{ \$11,620.04}`

Therefore, the future value is approximately $11,620.04