Question

Mr. Clark makes a deposit at the beginning of every year into a savings account that earns interest at 4.6% compounded annually. He saves for eight years, then converts his savings into an annuity that pays him $3,450 at the beginning of every year for three years. What is the size of the deposit he makes while he is saving? The size of the deposit is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) Determine the accumulated value after 8 years of deposits of $341.00 made at the beginning of every year and earning interest at 6%, with the payment and compounding intervals the same. The accumulated value is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

Given:

Interest Rate (r) = 4.6% per year, compounded annually

Number of periods (n) = 8 years

Annuity Payment (PMT) = $3,450 per year for 3 years

Using the formula for future value of an annuity:

FV = PMT * [(1 + r)^n - 1] / r

Plugging in the given values and solving for PMT:

$3,450 = PMT * [(1 + 0.046)^8 - 1] / 0.046

Solving for PMT:

PMT ≈ $3,450 / [(1.046^8 - 1) / 0.046]

PMT ≈ $3,450 / 6.456006

PMT ≈ $534.7298

Therefore, the size of the deposit Mr. Clark makes while he is saving is approximately $534.73 (rounded to the nearest cent).

To determine the accumulated value after 8 years of deposits of $341.00 made at the beginning of every year, we can use the future value of an annuity formula.