Question

2.

Kristen invests $5,000 in a bank. The bank pays 6% interest
compounded quarterly. Find, to the nearest cent, the balance
in the account after 5 years. To the nearest year, how long
must she leave the money in the bank for it to double?

Answer 1

1. ) $6,734.30

2) 12 years

Explanation:

1. we use the compound interest formula for this

Mathematically;

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

where P is the principal which is the amount deposited = $5,000

r = rate = 6% = 6/100 = 0.06

n = number of time per year we compound = 4 since it is quarterly

t = number of years = 5

Substituting all of these, we have;

A = 5,000( 1 + 0.06/4)^(4)(5)

A = 5,000( 1 + 0.015)^20

A = 5,000(1.015)^20

A = $6,734.28 which to the nearest cent = $6,734.30

2) For the money to double means that A becomes 2P

Thus;

2P = P( 1 + 0.015)^4t

divide both sides by P

2 = (1.015)^4t

Fine the ln of both sides

ln 2 = 4t ln 1.015

divide both sides by ln 1.015

4t = ln 2/ ln 1.015

4t = 46.56

t = 46.56/4

t = 11.63 which is approximately 12 years