For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response.

Question

Part A: You want to find the future amount of an account after $8,200 was invested at 6.5% compounded annually after a certain number of years. Define bo and r .

Part B: Write a recursive formula to show how much will be in the account after n years.

Part C: How much will be in the account at the end of 2 years? Round to the nearest cent. Be sure to show your work to support your answer.

Answer 1

A= 8200(1.065)^t where t = number of years

general formula is

A=P(1+r/n)^nt, but since n=1 = number of compounding periods annually, the formula reduces to

A=P(1+r)^t

P=starting amount = 8200

A=ending amount

t = time measured in years

it's a geometric sequence with common ratio = 1.065, so

use sum of a geometric sequence formula

Sn = a(1-r^n)/(1-r) = a(r^n-1)/r-1)

= 8200(1.065^n -1)/.065

after 2 years

A= 8200(1.065)^2= 9300.645

= about $9,300.65