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Write equations showing the total amounts of money that John and Carla would have withdrawn if they close their accounts in “n” years.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