Question

amila plans to go for vacation to Australia in 12 years from now. She estimates that she will need $23,840 for the trip. How much does she need to place in a saving account today that earns 3.21 percent per year (compounded quarterly) to accumulate this amount? Round the answer to two decimal places

Answer 1

Ans. Formula to compute future value of sum invested at a rate of r for t number of years compounded n times,

FV = PV * (1+r/n)^nt

FV = Future value = $ 23,840

PV = Present value = ?

r = rate of interest = 3.21%

t = number of years = 12 years

n = number of time compounded per year = 4

Insert above data in the formula

PV = FV / (1+r/n)^nt

= 23,840 / (1+3.21/100*1/4)^4*12

= 23840 / (1+3.21/400)⁴⁸

= 23840 * 1/(0.008025)⁴⁸

= 23840 * 0.681361

= 16243.65