Question

Suppose that $5,000 is placed in a bank account at the end of each quarter over the next 14 years. What is the future worth at the end of 14 years when the interest rate is 13% Compounded at the given intervals?

(a). Quarterly

Answer 1

(a).

For Quarterly

Given information,

Deposit amount = $5,000

Number of years = 14 years (Compounded quarterly) = 14 * 4 = 56 periods

Interest rate = 13% (Compounded quarterly) 13% / 4 = 3.25%

Here We have to to find the Future value annuity For this we can use the following formula:

Future value annuity = P * [(1 + r)ⁿ - 1] / r.................(1)

Here,

P = periodic payment = $5,000

r = Rate of interest = 3.25% = 0.0325

N = number of periods = 56 periods

Substuting the respective value in the formula (1)

Future value annnnuity = P * [(1 + r)ⁿ - 1] / r

= $5,000 * [(1 + 0.0325)⁵⁶ - 1] / 0.0325

= $5000 * [(5.9957480985) - 1] / 0.0325

= $5,000 *(4.9957480985) / 0.0325

= $5,000 * 153.7153261084

= $ 5768,576.6305422

So the the future worth will be $5768,576.63 (Quarterly).