Business Math

[askmemath]

In continuance with my policy of getting dazed in my Business Math class, I present to you another problem

Irina deposited $200 at the end of each month in an annuity that pays 6.5% compounded monthly. At the end of 5 years, the interest rate increased to 7.75% compounded monthly. Irina continued the same deposit for another 7 years. What is the amount of her annuity on the date of her last deposit?

In class we are using the Formula A=R[(1+i)^n-1] / i
A=The Amount in dollars
R=Regular Deposits
i= Interest
n= Number of compounding periods[60 + 84 months right?]

So basically I just substitute? I mean, I calculate first for 5 years at 6.5% and then add to the 2nd for 7 years at 7.5%?

 

[Denis]

In continuance with my policy of getting dazed in my Business Math class, I present to you another problem
Irina deposited $200 at the end of each month in an annuity that pays 6.5% compounded monthly. At the end of 5 years, the interest rate increased to 7.75% compounded monthly. Irina continued the same deposit for another 7 years. What is the amount of her annuity on the date of her last deposit?
In class we are using the Formula A=R[(1+i)^n-1] / i
A=The Amount in dollars
R=Regular Deposits
i= Interest
n= Number of compounding periods[60 + 84 months right?]
So basically I just substitute? I mean, I calculate first for 5 years at 6.5% and then add to the 2nd for 7 years at 7.5%?

i = .065/12, n = 5*12 = 60 :
A = 200[(1+i)^n-1] / i
That'll amount to 14134.79~

That amount starts earning 7.75%, for 7 years:
i = .0775/12, n = 7*12 = 84
14134.79(1 + i)^84 = 24273.73~ : that's what the 14134.79 will accumulate to

Now we need the accumulation of $200 monthly for 84 months:
A = 200[(1+i)^n-1] / i
That'll amount to 22213.29~

So total annuity = 24273.73 + 22213.29 = 46487.02~