# Compound Interest Calculation

#### kolag22

##### New member
Hi, I have a question regarding compound interest.
I have created compound table but also wanted to find a formula to work out an equation of what someone will need to make each year
on their investments to hit a certain target.

For example: If Peter had £137,000 in savings and wanted to have £800,000 at retirement in 28 years, how much interest will he need to make
on his starting amount each year. The profits/interest will be reinvested every year.

Does anyone know the formula to work this out?

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi, I have a question regarding compound interest.
I have created compound table but also wanted to find a formula to work out an equation of what someone will need to make each year
on their investments to hit a certain target.

For example: If Peter had £137,000 in savings and wanted to have £800,000 at retirement in 28 years, how much interest will he need to make
on his starting amount each year. The profits/interest will be reinvested every year.

Does anyone know the formula to work this out?
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

• kolag22

#### JeffM

##### Elite Member
Hi, I have a question regarding compound interest.
I have created compound table but also wanted to find a formula to work out an equation of what someone will need to make each year
on their investments to hit a certain target.

For example: If Peter had £137,000 in savings and wanted to have £800,000 at retirement in 28 years, how much interest will he need to make
on his starting amount each year. The profits/interest will be reinvested every year.

Does anyone know the formula to work this out?
$$\displaystyle 137(1 + r)^{28} = 800 \implies (1 + r)^{28} = 800/137 \implies \\ 1 + r = \sqrt{800/137} \implies r = \sqrt{800/137} - 1 \approx 0.065.$$
About 6.5% p. a. This assumes no taxes on the annual earnings. It is not a realistic model.

• kolag22

#### kolag22

##### New member
$$\displaystyle 137(1 + r)^{28} = 800 \implies (1 + r)^{28} = 800/137 \implies \\ 1 + r = \sqrt{800/137} \implies r = \sqrt{800/137} - 1 \approx 0.065.$$
About 6.5% p. a. This assumes no taxes on the annual earnings. It is not a realistic model.
Thank you for this @JeffM .
I will be going through this to see if this resolves my issue.