Use the Formula for the Sum of the First n Terms of a Geometric Sequence

Question

To save money for a sabbatical to earn a​ master's degree, Henry deposits ​$1400 at the end of each year in an annuity that pays 6.4 ​% compounded annually. Use the formula for the value of an​ annuity, shown to the right.

​

Formula: A=[(1+r/n)^nt-1])/r/n

​

a. How much will he have saved at the end of ​years?

b. Find the interest.

Answer 1

I don't know what the years are but I can show you how to solve this:

a. the formula should be A=P((1+r/n)^nt-1)/(r/n), A is future value (what we are looking for), P is the amount he deposits each period (1400), r is interest rate (.064), n is compounding periods (annually so 1), t is time in years. Now let's plug in the values:

A=1400((1+.064/1)^1*t-1)/(.064/1),1400/.064*((1.064)^t-1)=21875(1.064^t-1)

b. the amount of interest would be the answer to a - the amount of money he deposited (1400t)

interest=21875(1.064^t-1)-1400t