Question

2.1.9 Question Help An initial investment amount P, an annual interest rater, and a time t are given. Find the future value of the investment when interest is compounded (a) annually. (b) monthly, (c) daily, and (d) continuously. Then find (e) the doubling time T for the given interest rate. P = $2500, r=3.95%, t = 8 yr a) The future value of the investment when interest is compounded annually is $ (Type an integer or a decimal. Round to the nearest cent as needed.)

Answer 1

The future value of the investment when interest is compounded

(a) annually; A = $3,408.29

(b) monthly; A = $3,427.30

(c) daily; A = $3,429.02

(d) continuously; A = $3,429.08

e) the doubling time T; t = 17.54803 years

What is the future value?

P = $2500,

r=3.95% = 0.0395

t = 8 yr

A. Annually

`{A = P(1 + (r)/(n) )}^(nt)`

`A = {2,500.00(1 + (0.0395)/(1) )}^((1 * 8))`

A = 2,500.00(1 + 0.0395)⁸

A = 2,500.00(1.0395)⁸

A = $3,408.29

B. Monthly

`{A = P(1 + (r)/(n) )}^(nt)`

`A = {2,500.00(1 + (0.0395)/(12) )}^((12 * 8))`

A = 2,500.00(1 + 0.0032916666666667)⁹⁶

A = 2,500.00(1.0032916666667)⁹⁶

A = $3,427.30

C. Daily

`{A = P(1 + (r)/(n) )}^(nt)`

`A = {2,500.00(1 + (0.0395)/(365) )}^((365 * 8))`

A = 2,500.00(1 + 0.00010821917808219)²⁹²⁰

A = 2,500.00(1.0001082191781)²⁹²⁰

A = $3,429.02

D. Continuously

`{A = Pe}^(rt)`

`{A = 2,500.00(2.71828)}^((0.0395 * 8))`

A = $3,429.08

E.

Doubling time, t when A = 2P

= 2(2,500)

= $5,000.00

t = ln(A/P) / r

t = ln(5,000.00/2,500.00) / 0.0395

t = 17.54803 years

Answer 2

(a) $3408.29

Step-by-step explanation:

The future value of the investment can be calculated as:

`A=P(1+r)^t`

Where A is the future value, P is the initial investment, r is the interest rate and t is the period of time.

So, replacing P by 2500, r = 0.0395 and t by 8, we get:

`\begin{gathered} A=2500(1+0.0395)^8 \\ A=2500(1.3633) \\ A=3408.29 \end{gathered}`

Therefore, the future value of the investment is $3408.29