Question

Mr Chan’s son is three years old now and will be going to college in 15 years. Mr Chan would like to have $625,000 in a savings account to fund his education at that time. If the account promises to pay a fixed interest rate of 3% per year, how much money does Mr Chan need to put in the account today to ensure that he will have $625,000 in 15 years?

Answer 1

Solution:           

The formula for calculating the future value of an Investment with compound Interest is

FV = P * [ ( 1 + (r/n) ) ^{n * t} ]

Where

FV = Future value of Investment   ; P = Principal Investment today   ;   r = rate of interest   ;

n = No. of compounding periods per year ; t = Time in years

As per the information given in the question we have

FV = $ 625,000   ;   r = 3 % = 0.03 ; n = 1 ( Since compounding is yearly ) ;  

t = 15 Years ; P = $ To find    ;

Applying the above values in the formula we have

$ 625,000 = P * ( ( 1 + 0.03) / 1 )^{1 *15}             

$ 625,000 = P * ( 1.03 ) ¹⁵

$ 625,000 = P * 1.557967

P = $ 625,000 / 1.557967

P = $ 401,163.72

Thus the amount that should be invested by Mr. Chan today = $ 401,163.72

Note : ( 1.03 ) ^{( 15 )} = 1.557967 is calculated using the excel formula =POWER(Number,Power)

=POWER(1.03,15)