Question

Ann and Tom want to establish a fund for their grandson's education. what lump sum must they deposit at a 7% annual interest rate compounded monthly in order to have $60,000 in the fund at the end of 10 years?

Answer 1

Formula to calculate Principal with clompound interest:

`\begin{gathered} P=(A)/((1+(r)/(n))^(n\cdot t)) \\ \\ A=\text{Amount} \\ r=\text{Interest rate (decimals)} \\ n=\text{ number of times per unit t} \\ t=time \end{gathered}`

For the given situation:

A= 60,000

r= 7% =7/100= 0.07

n= 12 (as it is compounded monthly and a year has 12 months)

t= 10 years

`\begin{gathered} P=(60,000)/((1+(0.07)/(12))^(12\cdot10)) \\ \\ =(60,000)/((1+(0.07)/(12))^(120)) \\ \\ \approx29,855.78 \end{gathered}`

Then, they must deposit approximately $29,855.75