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 + }\frac{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