tamika opened a money market account that has 4.255 annual interest rat compounded annually.she deposits 1750 into the account each year.how much interest will the account earn after 15 years?

Question

its financial algebra

Answer 1

After the first year she will accumulate 1750×1.04255.

Then she will make another deposit of 1750, making the total amount 1750×1.04255+1750.

By the end of the second year she will have accumulated (1750×1.04255+1750)×1.04255.

Expanding this we get: 1750×1.04255²+1750×1.04255.

After fifteen years we have 1750×1.04255¹⁵+1750×1.04255¹⁴+...+1750×1.04255²+1750×1.04255.

This can be written 1750×1.04255(1.04255¹⁵-1)/(1.04255-1) (sum of a geometric progression).

This evaluates to 37,232.29. But, to find the interest we have to subtract the total amount invested which is 15×1750=26,250. So the interest is 10,982.29.