Question

1a.) Determine when, to the nearest year, $2,000 invested at 5% per year, compounded daily, will be worth $10,000.

1b.)Calculate, to the nearest cent, the future value FV (in dollars) of an investment of $10,000 at the stated interest rate after the stated amount of time.

6% per year, compounded daily (assume 365 days/year), after 12 years

1c.) Compute the specified quantity.

The simple interest on a $2,000 loan at 2% per year amounted to $360. At what time t did the loan mature (in years)?

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.

10,000=2000*(1+0.05/365)^(365n)

(10,000/2000)=(1+0.05/365)^(365n)

5=(1+0.05/365)^(365n)

Taking log on both sides;

log 5=365n*log 1.00013699

n=1/365[log 5/log 1.00013699]

=32 years(Approx)

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

A=10,000*(1+0.06/365)^(365*12)

=10,000*2.05431165

=$20543.12(Approx)

c.Simple interest=Principal*Interest rate*time period

360=2000*2%*time period

360=40*time period

time period=360/40

=9 years