# Another Financial Mathematics Question

**Question**

John saved $600 and Carla saved $550 into a savings account.

John found an account that would pay interest at 8% and Carla found a interest of 7% but earned interest over the interest she had. How much money would they both receive at the end of year 1 and at the end of year 2.

Write equations showing the total amounts of money that John and Carla would have withdrawn if they close their accounts in “n” years.

**Answer**

The general equations are like this :

For “no interest earned over interest” ( as in John’s case ), its called “simple interest”. With

A(n) = the accumulated value after end years at the end of the nth year,

A = the initial amount

and n= time in years,

i = interest in decimal value.

A(n) = A (1 + in)

For ” interest earned over interest” ( as in Carla’s case ), its called “compound interest”. With

A(n) = the accumulated value after n years at the end of nth year,

A = the initial amount

and n = time in years,

i = interest in decimal value.

A(n) =A ( 1 + i ) ^ n

That’s it.

In the example above for at the end of year 1,

John has A(1) = A (1+ in ) = 600(1 + (0.08)(1)) = $ 648

Carla has A(1) = A( 1 + i ) ^ n = 550(1+0.07)^1 = $ 588.5

Similarly,

In the example above for at the end of year 2,

John has A(1) = A (1+ in) = 600(1 + (0.08)(2)) = $ 696

Carla has A(1) = A( 1 + i ) ^ n = 550(1+0.07)^2 = $ 629.695