Question

A problem is listed below. Identify its type. Tammy wishes to purchase a new laptop in 4 years. She makes quarterly deposits of $100 into an account that pays 3% per year compounded quarterly for 4 years. How much will she have towards the purchase of a new laptop in 4 years?

Answer 1

At the end of 4 years, she will have $54933

Explanation:

Given-

Time to buy a new laptop, n = 4years

Quarterly deposit, C = $100 X 4 = $400 per year

Pays 3% per year compounded quarterly

We have to find the future value of Annuity

$FV = C * [\frac{(1 + i)^n - 1}{i} ]$

Where, C = cash flow

             i = interest rate

            n = number of deposits

$FV = 400 [ \frac{(1 + 3/400)^4}{3/400} ]\\\\FV = 400 [ \frac{1.03}{0.0075} ]\\\\FV = 400 * 137.33\\FV = 54933$

At the end of 4 years, she will have $54933