Math Help For College

Question

 richard and colleen want to save for a boat.they estimate that they,ll need about $4,5000 in 7 years.their bank offers a 2% interest rate compounded semiannually. how much would they need to deposit now in order to have $4,500 in 7 years

Answer 1

The formula for compound interest is

 

A = P (1 + r/f)^nf

 

A = Final amount

P = Starting amount

r = annual interest rate, as a decimal, not a percent

n = number of years

f = number of compounding periods per year

 

So in this case...

 

A = 4500, what they will need

P = to be determined

r = .02, which is 2%

n = 7

f = 2, since the compounding is done twice a year.

 

So 4500 = P(1 + .02/2)^7*2 = P(1.01)¹⁴

 

So 4500 / (1.01)¹⁴= P

 

3914.83 = P

 

So they would need to deposit $3,914.83

 

 

Answer 2

Cacynthia,

 

Assume they need to invest $P now

 

so 4500 = p(1+2/(100*2))^14

4500 = p(1.01)^14

p = 4500/(1.01)^14 = 3914.83

 

So they need to invest $3914.83