Use the compound interest formulas A=P(1+r/n)

Question

Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve.

 

Find the accumulated value of an investment of $10,000 at 7.5% compounded semiannually for 8 years.

Answer 1

in the first case, A - P[(1 + r/n)^nt], P = $10,000, r = 7.5% as a decimal, 0.075, n = compound periods per year, in this case semiannually = 2, and t = 8

 

the expression becomes A = $10,000 [(1 + 0.075/2)^(2*8)], which becomes $10,000 [[(1 + 0.075/2)¹⁶],

which becomes $10,000 (1.8022), which yields $18,022

 

with the second formula, P = $10,000, e = 2.718, r = 0.075, t = 8 ( e is a constant with a value of 2.718)

so, A = $10,000 (2.718)^(0.075*8)

A = $10,000 (2.718)^0.6

A = $10,000 (1.822)

the result is $18,220

Answer 2

the underlying formula that you want to use here is

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

for this set of parameters that means taking

A = 10000(1 + 0.075/2)^(2*8)

A = 10000(1.0375)^16

A = 10000(1.802228)

A = 18022.28

meaning that the accumulated value of the investment after 8 years is $18,022.28