Question

Odette deposited $3,624.40 into a savings account with an interest rate of 2.1% compounded annual. About how long will it take for the account to be worth $7,000?

A. 31 years, 9 months

B. 30 years, 9 months

C. 28 years, 4 months

Answer 1

Option A is the answer.

Explanation:

p = 3624.40

r = 2.1% or 0.021

n = 1

t = ?

A = 7000

Compound interest formula is :

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

Substituting the values in formula:

`7000=3624.40(1+(0.021)/(1))^(t)`

=>
`(7000)/(3624.40) =(1.021)^(t)`

=>
`1.93135=(1.021)^(t)`

`t=(log1.93135)/(log1.021)`

=> t = 31.670 years.

Closest to option A.

Answer 2

7000 = 3624*(1+0.21)^x

7000 = 3624 *1.021^x

7000/3624 = 1.021^x

875/453 = 1.021^x

xlog(1.021 = log(875/453

x = 31.677

31 years 9 months