Question

how long Will it take for $7000 investment to grow to $7553 and the annual rate of 3.4% compounded quarterly assume that no withdrawals are made

Answer 1

`t=2.25\ years`

Explanation:

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=?\ years\\ P=\$7,000\\ r=0.034\\n=4\\A=\$7,553`

substitute in the formula above

`7,553=7,000(1+(0.034)/(4))^(4t)`

solve for t

`(7,553/7,000)=(1.0085)^(4t)`

`(1.079)=(1.0085)^(4t)`

Applying log both sides

`log(1.079)=log[(1.0085)^(4t)]`

`log(1.079)=(4t)log(1.0085)`

`t=log(1.079)=[(4)log(1.0085)]`

`t=2.25\ years`