Question

Sara has just graduated from college. She has determined that to purchase a home in 10 years she needs to accumulate $42,400 for a down payment. If Sara can earn 4% per year on her savings, what is the amount of the annual annuity payment that Sara must make at the end of each year for 10 years?

Answer 1

Answer:

Periodic payment = $3,531.54

Explanation:

Given:

Future value = $42,400

Rate (r) = 4% = 0.04

Number of year (n) = 10

Pmt = periodic payment = ?

Computation of periodic payment:

$Future \ value = Pmt[\frac{(1+r)^n-1}{r} ]\\\\42,400 = Pmt[\frac{(1+0.04)^{10}-1}{0.04} ]\\\\42,400 = Pmt[\frac{(1.04)^{10}-1}{0.04} ]\\\\42,400 = Pmt[\frac{1.48024428-1}{0.04} ]\\\\42,400 = Pmt[\frac{0.48024428}{0.04} ]\\\\42,400 = Pmt[12.006107]\\\\\frac{42,400}{12.006107}= Pmt \\\\Pmt = 3,531.536$

Periodic payment = $3,531.54