How do I tackle this problem?

[rozzer123]

Hi all,

I've been studying for a math exam on financial maths - mainly compound interest. Usually, I'm asked to simply solve for the interest rate, future value, etc. But, I've come across this problem which I am really stuck on.

Angelina deposits $3000 in a savings account on 1 January 2019, earning compound interest of 1.5% per year.

a). Calculate how much interest (to the nearest dollar) Angelina would earn after 10 years if she leaves the money alone.

I understand that with this problem, I can simply apply the compound interest formula to solve for the value. 3000 * (1+1.5/100)^10

b). In addition to the $3000 deposited on January 1st 2019, Angelina deposits a further amount of $1200 into the same account on an annual basis, beginning on 1st January 2020. Calculate the total amount of money in her account at the start of January 2030 (before she has deposited her money for that year).

However, for this one, I am not sure as to how I should tackle the question. For the beginning of 2020, you end up with $3000 compounded by the interest rate, plus the $1200 deposit, right? So, how would I apply the compound formula in this case?

I've tried to solve it like this:

Beginning of:

2019 = 3000
2020 = 3000*1.015 + 1200
2021 = (3000*1.015 + 1200) * 1.015 + 1200... but I can't come up with a general formula for this pattern.

Would this be a formula?

(1800+1200n) * (1+1.5/100)^11... (I've become very confused and am not sure if I am even solving for the right value).

Any help or advice would be appreciated!

 

[tkhunny]

Please create a time map, sort of like you did, but just locate the individual cash flows. No need to stop at every intermediate accumulation.

Beginning
2019 $3,000
2020 $1,200
2021 $1,200
2022 $1,200
2023 $1,200
2024 $1,200
2025 $1,200
2026 $1,200
2027 $1,200
2028 $1,200
2029 $1,200

That's all you need to start. Now, we know where every cash flow happens.

Next, move EACH PIECE up to the valuation date:

2019 $3,000*(1.015)^11
2020 $1,200*(1.015)^10
2021 $1,200*(1.015)^9
2022 $1,200*(1.015)^8
2023 $1,200*(1.015)^7
2024 $1,200*(1.015)^6
2025 $1,200*(1.015)^5
2026 $1,200*(1.015)^4
2027 $1,200*(1.015)^3
2028 $1,200*(1.015)^2
2029 $1,200*(1.015)^1

See how this reflects the value of EACH deposit on the date that you want it?

Finally, simply add them up. I'll leave this for you. Don't you DARE calculate each value separately. Remember why you studied Geometric Series.

 

[rozzer123]

I see! Creating a timeline really does help. Thank you so much!

 

[Harry_the_cat]

Hi all,

I've been studying for a math exam on financial maths - mainly compound interest. Usually, I'm asked to simply solve for the interest rate, future value, etc. But, I've come across this problem which I am really stuck on.

Angelina deposits $3000 in a savings account on 1 January 2019, earning compound interest of 1.5% per year.

a). Calculate how much interest (to the nearest dollar) Angelina would earn after 10 years if she leaves the money alone.

I understand that with this problem, I can simply apply the compound interest formula to solve for the value. 3000 * (1+1.5/100)^10

This calculation will give you the total amount of Angelina's investment after 10 years. What do you need to do then to calculate how much interest she earned?