Check my answers?

Question

A certain bank pays 1% compound interest for their savings account holders. If Nick deposits $10000 in that bank.

a) Write down the formula for the Yield.
A = P(1+r)^t

b) Explain the meaning of each variable in the formula.

P = Starting Principle
r = Interest rate
t = Time Period
A = Ending Balance

c) Estimate how much money will be in his account after 25 years using your formula. Assume there will not be any deposits or withdrawals during that 25 year period.

A = 12,824.32

d) Estimate how long it will take to double the total amount in Nick’s account.

Using the equation: A = P(1+r)^t

If this account compounds once per year @ 1%, then
when: t = 69.66 yrs. will yield A = $19,999.86
when: t = 69.67 yrs. will yield A = $20,001.85
Approx. 69.665 yrs.

e) Estimate the total amount in Nick’s account after one year.

A = 10,100

ln(2)=tln(1+r)
t=ln(1+r)/ln(2)

I don't get the "In" part of the equation. How does that work?

Answer 1

(a) and (b) are correct and there is no assumption here about what time period is being used. For example t would be in years if interest is compounded annually but t would be in months if interest is compounded monthly.

So for (c) you are assuming that interest is compounded annually, which is probably right but something you should note.

(d) A quick way to do this is to solve for t where A=2P

A=P(1+r)^t
2P=P(1+r)^t
2=(1+r)^t
ln(2)=tln(1+r)
t=ln(1+r)/ln(2)

again (e) is correct as long as interest is compounded annually.

Answer 2

Just a point of clarification..
In the formula A = P(1+r)^t
r is the rate interest accrues during each compound period, and t is the number or compounding periods.
For example, if the APR is 12% and you wanted to know A at the end of the year, it would be incorrect to use t = 1 and r = .12 if the compound period was 1 month. Over the period of a year, r would .01, and t would be 12 in my example.

I'm sure you know this, but I just wanted to make sure you get the definitions correct. I didn't check the arithmetic. Everybody else has done that.

Answer 3

You look fine to me.

Answer 4

c)O.K
d) At start A=P
At time t you have 2A=A(1.01)^t
so taking ln ln2=t*ln (1.01 ln2/ln(1.01)=t = 69.6607years
d)O.K