Question

Bob makes his first $ 800 deposit into an IRA earning 7.4 % compounded annually on his 24th birthday and his last $ 800 deposit on his 39th birthday ​(16 equal deposits in​ all). With no additional​ deposits, the money in the IRA continues to earn 7.4 % interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob​ retires?

Answer 1

Answer:The answer is $17,387.67

Step-by-step explanation:

Let Principal = P, Rate = R% per annum, Time = n years

Amount = P ( 1 + R/100)∧n

P = $800, R = 7.4%, n = 24

A = 800 ( 1 + 7.4/100)∧24

A = 800 ( 1 + 0.074)∧24

A = 800 ( 1 .074)∧24

A = 800 (5.547569512)

A = 800× 5.5475569512

A = $4,438.05

Deposit made at 39th birthday

P = $800, R = 7.4%, n = 39

A = 800 ( 1 + 7.4/100)∧39

A = 800 (1 + 0.074)∧39

A = 800 (1.074)∧39

A = 800 (16.187022604)

A = 800× 16.187022604

A = $12,949.62

How much is in the IRA when Bob retires will be

$4,438.05 + 12,949.62

= $17,387.67