Question

Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.

Answer 1

Annette Michaelson will need $11,000 in 8 years to help pay for her education. Determine the lump sum, deposited today at 4.5% compounded monthly, will produce the necessary amount.​

we know that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

A=11,000

t=8 years

n=12

r=4.5%=0.045

substitute in the formula above

`\begin{gathered} 11,000=P(1+(0.045)/(12))^((12\cdot8)) \\ 11,000=P((12.045)/(12))^((96)) \\ \\ P=7,679.61 \end{gathered}`

therefore

the answer is

$7,679.61therefore