Question

Calculate the amount to be saved at the beginning of each year for 18 years, in order to accumulate $45,000 for each of the twins education, assuming a discount rate of 12% on their savings. They will commence their university study in the month of January. If instead, they save money at the end of the year, how much do they have to put aside to meet the same education funding goal?

Answer 1

Amount required in 18 years (Future value) =45000*2=   $90,000
Time in years (n) =   18
Interest rate (r) is 12% or   0.12

Payment starts from beginning of month. so it is Annuity due  
Future value of annuity due formula = P *(1+r) *{ (1+r)^n - 1 } / r   
90000 = P*(1+0.12)*( ((1+0.12)^18)-1)/0.12  
90000=P*   62.43968075
P =   1,441.39

So, size of payment is   $1,441.39

(B) if Payment starts from end of year, it is ordinary Annuity.

Future value of annuity formula = P *{ (1+r)^n - 1 } / r   
90000 = P*( ((1+0.12)^18)-1)/0.12  
90000=P*   55.74971496
P =   1,614.36

So, size of payment is   $1,614.36

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