Answer:
The question is incomplete:
Answer the following questions::
a. How long will it take this bank account to reach $10,000? Explain how you determined this and show your work.
b. Will you have enough money to buy the car 15 months from now? Will the account have some money left over?
a)
FV = PV x e^rn
FV = future value
PV = present value
e = 2.7183 (always)
r = interest rate
n = time
10,000 = 9,359.08 x 2.7183⁰°⁰⁵ⁿ
2.7183⁰°⁰⁵ⁿ = 10,000 / 9,359.08 = 1.06848109
ln 2.7183⁰°⁰⁵ⁿ = ln 1.06848109
0.05n = 0.066238097
n = 0.066238097 / 0.05 = 1.3248 years
1.3248 years = 1 year, 3 months and 27 days
b)
Since it takes 1 year, 3 months and 27 days to have $10,000, you will not have enough money if you leave it there for 15 months. Total balance at the end of 15 months:
FV = 9,359.08 x 2.7183⁽⁰°⁰⁵ ˣ ¹°²⁵⁾
FV = 9,359.08 x 2.7183⁰°⁰⁶²⁵
FV = 9,359.08 x 1.064494904 = $9,962.69
