continuous compounding ... final amount = initial amount * e^(rate * time)
(a) amount = 700 * e^(.045 * 1) ≈ 732.22
When one rents an apartment, one is often required to give the landlord a security deposit that is returned if the apartment is undamaged when you leave. In some localities, the landlord is required to pay the tenant interest once a year compounded yearly. Assume that the landlord is required to pay the tenant interest of 5 % compounded annually.
(a) Suppose the landlord invests a security deposit of $ 700 at a rate of 4.5 % compounded continuously. What is his net gain or loss after one year, rounded to the nearest cent? Use a negative number to denote a loss.
b) Suppose the landlord invests a security deposit of $ 700 at a rate of 6.3 % compounded continuously. What is his net gain or loss after one year, rounded to the nearest cent? Use a negative number to denote a loss.
2 answers
If the landlord is investing the security deposit at a rate of 4.5% compounded continuously, then you would calculate the profits he makes using the formula P(t)=Poe^(r*t)
So,
P(t)=700e^(0.045*1)
P(t)=$732.22
The landlord makes $32.22 as a profit, but since he has to pay the tenant interest on their security deposit, you must subtract the interest as well.
P(t)=700(0.05)
P(t)=$35
Thus, if you subtract 35 from 32.22, you get $-2.78, which is the total loss.
Same thing for part B, just with different interest on the investment.
So,
P(t)=700e^(0.045*1)
P(t)=$732.22
The landlord makes $32.22 as a profit, but since he has to pay the tenant interest on their security deposit, you must subtract the interest as well.
P(t)=700(0.05)
P(t)=$35
Thus, if you subtract 35 from 32.22, you get $-2.78, which is the total loss.
Same thing for part B, just with different interest on the investment.