Please help me solve the following questions, they are follow ups for the first
ID: 2910763 • Letter: P
Question
Please help me solve the following questions, they are follow ups for the first question.
Full points will be awarded, thanks in advance!
5. Nora's grandfather just opened a savings account in Nora's name and deposited $1500 in the account. The savings account has an APR of 3%, compounded monthly (3 points) Find a formula that gives the balance, B, of Nora's account in dollars t years from today a. b. (4points) In what year will Nora's account balance hit $10,500? c. (3 points) Nora has her eye on a used car that is currently valued at $10,500. This type of car depreciates at a rate of 15% per year. Find a formula that gives the value, V, of this car t years from today d. (1 point) How much will the car be worth when Noah's account balance hits $10,500? (5 points) In what year will Nora have enough money in her savings account to be able to buy the car (accounting for the fact that the car is depreciating)? e.Explanation / Answer
P = 1500 $
r = 3%
compded monthly
So, formula is :
A = P(1 + r/12)^(12t)
where r = 3% or 0.03
and t = time in yrs
So,
A = 1500(1 + 0.03/12)^(12t)
B = 1500(1.0025)^(12t) ---> AMS
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b)
When will it hit 10500 eh?
Lets find out ....
10500 = 1500(1.0025)^(12t)
1.0025^(12t) = 7
12t * ln(1.0025) = ln(7)
t = 64.9447174837209805
So, it will hit it when t = 65 yrs --> ANS
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c)
Depreciates at 15%
So, A = P(1 - r)^t
V = P(1 - 0.15)^t
V = P(0.85)^t
V = 10500(0.85^t) ---> ANS
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d)
Plug in t = 65 :
V = 10500(0.85^65)
V = 0.2712810579818552
So, after 65 yrs,
the value is 0.27$
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e)
We are basically solvin for ...
1500(1.0025)^(12t) = 10500(0.85^t)
1.0025^(12t) = 7(0.85)^t
Logging both sides:
12t * log(1.0025) = log(7) + log(0.85)
12t = (log(7) + log(0.85)) / log(1.0025)
12t = 714.2478123566626653
So, t = 59.520651029721888775
So, she can buy it when t = 60 ---> ANS