Question

Suppose you deposited $4,000 in a savings account earning 2.0% interest compounding daily. How long will it take for the balance to grow to $11,000? Answer in years rounded to two decimal places. (e.g., 2.4315 years --> 2.43)

If the applicable discount rate is 5.0%, what is the present value of the following stream of cash flows? Round to the nearest cent.

Cash Flow Year 1: $1,000
Cash Flow Year 2: $5,000
Cash Flow Year 3: $6,000

You plan to deposit $5,000 today, $1,000 in one year and $5,000 in two years into an account earning 2.0% interest. What will the account balance be in 4 years? Round to the nearest cent.

Answer 1

a.We use the formula:  
A=P(1+r/365)^365n
where
A=future value
P=present value  
r=rate of interest
n=time period.

11000=4000*(1+0.02/365)^(365n)

(11000/4000)=(1+0.02/365)^(365n)

2.75=(1.00005479)^365n

Taking log on both sides;

log 2.75=365n*log 1.00005479

n=1/365[log 2.75/log 1.00005479]

=50.58 years(Approx).

b.Present value=Cash flows*Present value of discounting factor(rate%,time period)

=1000/1.05+5000/1.05^2+6000/1.05^3

=$10670.55(Approx)

c.We use the formula:  
A=P(1+r/100)^n
where
A=future value
P=present value  
r=rate of interest
n=time period.

A=5000*(1.02)^4+1000*(1.02)^3+5000*(1.02)^2

=$11675.37(Approx)