Question

An investment company pays 9​% compounded semiannually. You want to have $19000 in the future in 10 years

Answer 1

`\$7,878.21`

Explanation:

The question is

What is the amount of money to be invested now?

we know that

The compound interest formula is equal to

`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

`t=10\ years\\ A=\$19,000\\ r=9\%=9/100=0.09\\n=2`

substitute in the formula above

`19,000=P(1+(0.09)/(2))^(2*10)`

solve for P

`19,000=P(1.045)^(20)`

`P=19,000/(1.045)^(20)`

`P=\$7,878.21`