Answer:
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.