Answer to Question #203468 in Financial Math for Nico Renouf

Question

Melanie is deciding which of the two long term savings plan to choose for investing $9000: 6.2% per annum, compounding semi-annually, or 5.75% per annum compounded quarterly. If she plans to leave the money in the plan of 8 years, which is the better option?

Answer 1

$A = P(1 + \frac{r}{n})^{nt}$

In the formula

• A = Accrued amount (principal + interest)
• P = Principal amount
• r = Annual interest rate as a decimal
• n = number of compounding periods per unit of time
• t = time in decimal years

$A = P(1 + \frac{r}{n})^{nt}\\ A = 9,000.00(1 + \frac{0.062}{2})^{(2)(8)}\\ A = 9,000.00(1 + 0.031)^{(16)}\\ A = \$14,668.35$

Interest=amount-principal

$I=14668.35-9000=\$5668.35$

$A = 9,000.00(1 +\frac{ 0.0575}{4})^{(4)(8)}\\ A = 9,000.00(1 + 0.014375)^{(32)}\\ A = \$14,210.05$

Interest=amount-principal

$I=14210.05-9000=\$5210.05$

The first option is the best since its interest is high.