Q9 On January 1, 2010, you put €1000 in a savings account that pays 6.25 % interest, and you will do this every year for the next 18 years withdraw the balance on December 31, 2028, to pay for your child’s college education. How much will you withdraw
FV = (1+r) *P [(1+r)^n-1]/r
The future value of annuity due formula is used to calculate the ending value of a series of payments or cash flows where the first payment is received immediately. The first cash flow received immediately is what distinguishes an annuity due from an ordinary annuity. An annuity due is sometimes referred to as an immediate annuity.
Unclear from your question wording if 1 payment then 18 more or just 18 payments....this calc is for 19 payments...if it is 18 , just change the 19 to 18
Fv = (1+.0625) * 1000 [(1+.0625)^19-1]/.0625
Use this formula to calculate FV:
PV=0; P=1000; R=0.0625; N=18 FV =P*((1 + R)^N - 1)/ R * (1 +R)
=31, 647.58 x 1.0625 =$33,625.56 - this is based on the assumption that 18 deposits of 1,000 pounds are made - the last being on Jan. 1, 2028. Then the fund earns interest for 1 full year @ 6.25%. The 19th deposit on Jan. 1, 2029 is NOT made. This is where the deposits are made at the BEGINNING of the period and NOT at the END.
I do not think that formula is correct....this question has a payment on the First of the period not one period away:
THIS is about the formula that you posted:
The future value of an annuity formula is used to calculate what the value at a future date would be for a series of periodic payments.
The future value of an annuity formula assumes that
1. The rate does not change
2. The first payment is one period away
3. The periodic payment does not change
Here's what this website calculates (in dollars....the pounds would be the same ) :