Thomas rays parents begin saving to buy their son a car for his 16th birthday. they save $800 the first year and each year they save 5% more than the previous year. How much money will they have saved for his 16th birthday.

money they will have saved for his 16th birthday = $18,926

Step-by-step explanation:

This is a geometric series problem.

The sum of a geometric series is given by the formula;

Sn = a1• (rⁿ - 1) / (r - 1)

Where;

a1 is the first term

n is the number of terms

r is the constant ratio

Now, in this question, they started saving since he was born till his 16th birthday. That's 16 years. Thus number of terms; n = 16

Also, the first money saved was $800, thus the first term; a1 = 800

They save 5% more each year than the previous year. That's an increase of 1.05 each year. Thus, the common ratio; r = 1.05

The amount of money they will have by his 16th birthday will be;

S_16 = 800• (1.05^ (16) - 1) / (1.05 - 1)

S_16 = 800 (1.18287458838/0.05)

S_16 = $18,926

S16 = $800· (1.05^16 - 1) / (1.05 - 1)