Question

Suppose that $2500 is placed in a savings account at an annual rate of 5%, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the account to grow to $3500

Answer 1

Answer:

number of periods = 8 years.

Explanation:

We know,

Future Value = Present value × $(1 + r)^{n}$

Here,

Present value = PV = $2,500

Future value = FV = $3,500

Interest rate (Compounding) = 5% = 0.05

We have to determine how many years (Periods) it will take, n = ?

Putting the values into the above formula,

$3,500 = $2,500 × $(1 + 0.05)^{n}$

or, $(1 + 0.05)^{n}$ = $3,500 ÷ $2,500

or, n log 1.05 = 1.4

or, n × 0.17609 = 1.4

or, n =  1.4 ÷ 0.17609

Therefore, number of years = 7.95 or 8 years.