Question

Jackie makes an $800 deposit into a bank account earning 4.5% interest.

Answer 1

Answer:

a. $1251.5

b. $1254.64

c. 15.4 years

d. 30.56 years

Step-by-step explanation:

Given the information:

• Principle (P) = $800
• Interest = 4.5%

As we know, the formula to find the future value of Jackie deposit with interest is compounded monthly, quaterly, ..is

$A=P(1+\frac{r}{n} )^{nt}$  where:

• P = initial balance
• r = interest rate (decimal)  
• n = number of times compounded annually
• t = time

Hence:

a. If the interest is compounded quarterly how much money will Jackie have in 10 years?

$A=P(1+\frac{r}{n} )^{nt}$  

<=>  $A=800(1+\frac{0.045}{4} )^{4*10}$

<=> A = $1251.5

d. If Jackie's money is compounded monthly, how long will it take her money to triple?

<=> $A=P(1+\frac{r}{n} )^{nt} = 3*800$

<=> $800(1+\frac{0.045}{12} )^{12*t} = 2400$

<=> $(1+\frac{0.045}{12} )^{12*t} = 3$

<=> t = 30.56 years

As we know, the formula to find the future value of Jackie deposit with interest is compounded continuously

A = P*$e^{rt}$ where e is the mathematical constant approximated as 2.7183.

b. If the interest is compounded continuously how much money will Jackie have in 10 years?

<=> A = 800*$2.7183^{0.045*10}$

<=> A = $1254.64

C. If Jackie's money is compounded continuously, how long will it take her money to double?

<=> P*$e^{rt}$  = 2*800

<=> 800*$2.7183^{0.045*t}$ = 1600

<=> $2.7183^{0.045*t}$ = 2

<=> t = 15.4 years