Compound interest question

Question

At what nominal rate, compounded monthly, would $10,000 have to be invested to amount to $16,000 in 6 years?

Answer 1

the underlying formula that you want to use here is

A = P(1 + r/n)^nt

solving that for the variable of interest here (r) makes it

r = n[(A/P)^(1/nt) - 1]

for this particular scenario that means taking

r = 12[(16000/10000)^(1/12*6) - 1]

r = 12[(1.6)^72 - 1]

r = 0.0786 = 7.86%

Answer 2

Kiera,

 

Let the rate be R

 

P = A(1+r/100)^n

 

Here P = 16,000

 

A = 10,000

 

n = 6*12 = 72 (since interest is compounded monthly)

 

r = R/12 (Again since it is compounded monthly)

 

16,000 = 10,000*(1+r/12)^72

 

1.6 = (1+r/12)^72

 

(1+r/12) = 1.00655

 

r/12 = 0.00655

 

r = 0.0786

 

or r = 7.86%