Geometric sum - Alfred & interest-rate

[Rectifier]

Homework Statement

Alfred puts 985 USD on his bank account every time he has a birthday. Alfred just turned 48. He started to save money when he turned 35 (including 35th birthday). How much money is there on his savings-account if the interest-rate was 3.7% every year and that he had no money in that account when he started saving.

This problem was translated from Swedish. Sorry for possible grammatical and typographical errors.

Homework Equations

A geometrical sum can be written as:
$$S=\frac{x^{n+1}-1}{x-1}$$

The Attempt at a Solution

This looks lika a geometrical sum. This is the first problem in the chapter and I am already stuck.

Alfreds deposits (not sure if that's the right word) looked like this:
$$985 + 985 \cdot 1.037^1 + ... + 985 \cdot 1.037^m$$
I will explai why i wrote m there soon.

This can be written as:
$$Money = 985(1 +1.037^1 + ... + 1.037^m)$$

The problem I am having is the number that I have to put instead of m. Is it 12, 13 or 14 and what happens when I want to calculate the sum? Will the sum be:

$$Money = 985 \cdot S= 985 \cdot \frac{1.037^{m+1}-1}{1.037-1}$$

Please help me :(

Many thanks in advance!

 

[SammyS]

Homework Statement

Alfred puts 985 USD on his bank account every time he has a birthday. Alfred just turned 48. He started to save money when he turned 35 (including 35th birthday). How much money is there on his savings-account if the interest-rate was 3.7% every year and that he had no money in that account when he started saving.

This problem was translated from Swedish. Sorry for possible grammatical and typographical errors.

Homework Equations

A geometrical sum can be written as:
$$S=\frac{x^{n+1}-1}{x-1}$$

The Attempt at a Solution

This looks lika a geometrical sum. This is the first problem in the chapter and I am already stuck.

Alfreds deposits (not sure if that's the right word) looked like this:
$$985 + 985 \cdot 1.037^1 + ... + 985 \cdot 1.037^m$$
I will explai why i wrote m there soon.

This can be written as:
$$Money = 985(1 +1.037^1 + ... + 1.037^m)$$

The problem I am having is the number that I have to put instead of m. Is it 12, 13 or 14 and what happens when I want to calculate the sum? Will the sum be:

$$Money = 985 \cdot S= 985 \cdot \frac{1.037^{m+1}-1}{1.037-1}$$

Please help me :(

Many thanks in advance!

See what works for his 37th or 38th birthday -- something easy like that.

 

[Rectifier]

See what works for his 37th or 38th birthday -- something easy like that.

Lets say 37.

Then

Alfreds deposits would look like this:
$$985 + 985 \cdot 1.037^1 + 985 \cdot 1.037^2$$
37 36 35

This can be written as:
$$Money = 985(1 +1.037^1 + 1.037^2)$$

Does this mean that m=age now - age when he started saving
thus m=13?

 

[Ray Vickson]

Lets say 37.

Then

Alfreds deposits would look like this:
$$985 + 985 \cdot 1.037^1 + 985 \cdot 1.037^2$$
37 36 35

This can be written as:
$$Money = 985(1 +1.037^1 + 1.037^2)$$

Does this mean that m=age now - age when he started saving
thus m=13?

You tell us!

There is also the issue of whether you examine the account balance seconds before his birthday, or seconds after it; that will make a difference of 985 in the answer.

 

[Rectifier]

You tell us!

There is also the issue of whether you examine the account balance seconds before his birthday, or seconds after it; that will make a difference of 985 in the answer.

m=age now - age when he started saving

The one above (37)

m=37-35=2

Then this must mean that m in the problem is:
m=48-35=13

Am I right? :D

 

[Ray Vickson]

m=age now - age when he started saving

The one above (37)

m=37-35=2

Then this must mean that m in the problem is:
m=48-35=13

Am I right? :D

Make a table. Suppose we look at his balance immediately after his birthday. Then we have:
$$\begin{array}{c|l}<br /> & \text{Account}\\<br /> \text{Birthday} & \text{balance} \\<br /> 35 & 985 \\<br /> 36 & 985 + 985 \cdot 1.037 \\<br /> 37 & 985 + 985 \cdot 1.037 + 985 \cdot 1.037^2 \\<br /> \cdots & \cdots<br /> \end{array}$$
You can take it from there.

BTW: I recommend you do things in that somewhat detailed way to start with, until you gain a lot of experience with such problems. Jumping right away to plug-in formulas can be a mistake.

 

[SammyS]

m=age now - age when he started saving

The one above (37)

m=37-35=2

Then this must mean that m in the problem is:
m=48-35=13

Am I right? :D

Well, it works fine for 37th birthday, so why not for the 48th ?

 

[Thyphon]

F= the total money when he is 48
A= every birthday money that is 985
i= %3,7 =0,037
n=48-35=13
F=A(F/A,i,n)
F=985[(((1+i)^n)-1)/i]

is that true?

 

[Thyphon]

F= the total money when he is 48
A= every birthday money that is 985
i= %3,7 =0,037
n=48-35=13
F=A(F/A,i,n)
F=985[(((1+i^n)-1)/i]

is that true?

the formula is that