Question

If you invest $5,000 in months 2 and 3 in an account that earns 2.00% APR, compounded monthly, , how much can you withdraw (equal amounts) in months 5 and 6 ?

Answer 1

Investment of $5000 in 2 month

Time remaining to 4 months = 2 month

It means 2 months interest is earned.

Investment of $5000 in 3 month

Time remaining to 4 months = 1 month. 1 month earned will be earned.

Interest rate = 2% APR

Monthly rate = 0.02/12= 0.001666666667

We have to calculate first future value of amount deposited to find amout that present at 4 months and that future value will be present value for amount of withdrawl in 5 and 6 months

Future value = Present value *(1+i)^n

5000*(1+0.0016666667)^2 + 5000*(1+0.001666667)^1

10025.01389

So, Value of amount at end of 4th month is $10025.01389

Present value of annuity is $10025.01389, out of which 2 month annuity can be withdrawn.

Equal annuity payments formula = P* i *((1+i)^n)/((1+i)^n-1)

10025.01389*0.001666667*((1+0.001666667)^2)/((1+0.00166667)^2-1)

5025.03264

So, equal amount can be withdrawn for $5025.03