Compound interest a deposite of $1000 is made in an account that earns interest at an annual rate of 5%.how long will it take for the balance to double when the interest is compounded (a) annually,(b) monthly,(c) daily, and (d) continously?

(a) 14.21

(b) 13.78

(c) 13.57

(d) 13.86

Step-by-step explanation:

Compound Interest, compounded n times per year,

Compound Interest, compounded continuously,

Where

A is the new amount/balance

P is the Principal (amount invested)

r is the rate in percentage

n is the number of times it is compounded.

Given:

Principal, P = $1000

rate, r = 5% = 0.05

For the balance to double, A = 2 × $1000

                A = $2000

(a) annually, n = 1

To solve for t, we take of both sides

                    t = 14.21

(b) monthly, n = 12

To solve for t, we take of both sides

                    t = 13.78

(c) daily, n = 365

To solve for t, we take of both sides

                    t = 13.565

                    t = 13.57

(d) Continuously

To solve for t, we take of both sides

But log_{e}e = 1

                    In2 = 0.05t

                    t = 13.86

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

so the possibilities of the measurement of the side of the triangle are either it is longest side or not the longest side

when it is the longest side

s < 25 + 35s < 60

if it is not the longest side

35 < 25 + s10 < sso 10 < s < 60so the perimeter70 < p < 130