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

Answer 1

After 5 years, the investment should grow to $407,223

Step-by-step explanation:

the future value earned on a certain amount compounded semi-annually for a number of years is given by the formula:

`FV = PV(1+ (r)/(n) )^(nt)\\Where:\\FV = Future\ value\ =\ ??\\PV = Present\ Value\ =\ $250,000\\r = Interest\ rate\ =\ 10\% =\ 0.1\\n = number\ of\ compounding\ per\ year\ = semiannually\ =\ 2\\t = number\ of\ years\ =\ 5`

`FV = 250,000(1+ (0.1)/(2) )^((2*5))\\FV\ = 250,000(1.05)^(10)\\FV\ = 250,000(1.62889)\\FV\ = \$407,223.65`

Therefore, after 5 years, the investment should grow to $407,223