Question

OMG HELP

A savings account is started with an initial deposit of $700. The account earns 1.5% interest compounded annually.
(a) Write an equation to represent the amount of money in the account as a fraction of time in years
(b) Find the amount of time it takes for the account balance to reach $1,200. Show Your Work.

Answer 1

Explanation:

a) Initial amount deposited into the account is $700 This means that principal,

P = 700

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 1.5%. So

r = 1.5/100 = 0.015

The formula for compound interest is

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

A = total amount in the account at the end of t years. Therefore, an equation to represent the amount of money in the account as a fraction of time in years is

A = 700 (1+0.015/1)^1×t

A = 700(1.015)^t

b) when A = $1200,

1200 = 700(1.015)^t

1200/700 = 1.015^t

1.7143 = 1.015^t

Taking log of both sides

Log 1.7143 = log 1.015^t = tlog 1.015

0.2341 = 0.0065t

t = 0.2341/0.0065

t = 36 years