Question

Bob makes his first $1,300 deposit into an IRA earning 7.1% compounded annually on his 24th birthday and his last $ 1,300 deposit on his 40th birthday ​(17 equal deposits in​ all). With no additional​ deposits, the money in the IRA continues to earn 7.1 % interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob​ retires?

Answer 1

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value  
r=rate of interest  
n=time period.

A=1300*(1.071)^41+1300*(1.071)^40+1300*(1.071)^39+1300*(1.071)^38+1300*(1.071)^37+1300*(1.071)^36+1300*(1.071)^35+1300*(1.071)^34+1300*(1.071)^33+1300*(1.071)^32+1300*(1.071)^31+1300*(1.071)^30+1300*(1.071)^29+1300*(1.071)^28+1300*(1.071)^27+1300*(1.071)^26+1300*(1.071)^25

=1300*[(1.071)^41+(1.071)^40+(1.071)^39+(1.071)^38+(1.071)^37+(1.071)^36+(1.071)^35+(1.071)^34+(1.071)^33+(1.071)^32+(1.071)^31+(1.071)^30+(1.071)^29+(1.071)^28+(1.071)^27+(1.071)^26+(1.071)^25]

=1300*172.881547

=$224746.01(Approx)