Question

Angie invested $250,000 she received from her grandmother today in a fund that is expected to earn 10% per annum. To what amount should the investment grow in five years if interest is compounded semi-annually?

a. $407,223.
b. $387,835.
c. $442,890.
d. $402,625

Answer 1

The correct answer is:

$407,223. (a.)

Step-by-step explanation:

This question requires us to calculate the future value of a certain sum of money invested yielding a compound interest, and the formula for this calculation is given below:

FV =
`PV*(1 + (i)/(n) )^(n*t)`

where:

FV = future value = ???

PV = present value = $250,000

i = compound interest in decimal = 10% = 0.1

n = compounding period per year = semiannually = 2

t = compounding period in years = 5 years

∴ FV =
`250,000*(1 + (0.1)/(2) )^((2*5))`

FV = 250,000 ×
`1.05^(10)`

FV = 250,000 × 1.62889466268 = 407,223.65