Question

Your rich playful uncle makes you a proposition. he says hell give you 1000 if you cqn tell him how much money each of the following options would make.He’ll give you 10000 to deposit in a account. The account pays a 3.5% Interest compounded at the end of each year. You get to keep the amount of money in the bank at the end of the 15th year. He’ll give you one dollar the first day, two dollars the second, and three dollars the third. So on and so on, for the next 15 years. Which is a better option? Explain your answer or your uncle won’t give you your money.

Answer 1

The first option :

10000 to deposit in a account.

The account pays a 3.5% Interest compounded at the end of each year.

We need to find the money at the end of 15th year

So, P = 10,000 , r = 3.5% = 0.035 , t = 15 years

so,

`\begin{gathered} A=P\cdot(1+r)^t=10000\cdot(1+0.035)^(15) \\ A=10000\cdot1.035^(15)=16,753.5^{}^{}_{}^{} \end{gathered}`

The second option:

He’ll give you one dollar the first day, two dollars the second, and three dollars the third. So on and so on, for the next 15 years.

So, it will represent an arithmetic sequence : 1 , 2 , 3 , ..... and so on

the first term = a = 1 , the common difference = d = 1

So, the rule of the sequence will be:

`A(n)=a+d(n-1)`

The number of days of the year = 365

So, for 15 years

The number of days = 15 * 365 = 5,475 days

So, we need to find the sum of the sequence for 15 years

at the last day of 15 years , he will give him:

`1+1\cdot(5475-1)=5,475`

So, the sum will be:

`n\cdot(a1+an)/(2)=5475\cdot(1+5475)/(2)=5475\cdot2738=14,990,550`

So, the better option is the second