Question

If $4200 is invested in savings account for which interest is compounded semianually, and if the $4200 turns into $4900 in 4 years , what is the interest rate of the savings account

Answer 1

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

A=final amount

P=initial amount invested

r=rate in decimal form

n=number of times compounded per year

t=time in years

given

A=4900

P=4200

r=r (we are solving for this)

n=semianually=2 times per year

t=4

find r

`4900=4200(1+(r)/(2))^(2*4)`

`4900=4200(1+(r)/(2))^8`

divide both sides by 4200

`(4900)/(4200)=(1+(r)/(2))^8`

take 8th root of both sides

`\sqrt[8]{(49)/(42)}=1+(r)/(2)`

minus 1

`-1+\sqrt[8]{(49)/(42)}=(r)/(2)`

multiply both sides by 2

`-2+2\sqrt[8]{(49)/(42)}=r`

r=0.038911

r=3.891% so about 3.89%