Carlos invested $7,000 in a money market mutual fund that pays interest on a daily basis. The balance in his account at the end of 8 mo (245 days) was $7,432. Find the effective rate at which Carlos's account earned interest over this period (assume a 365-day year).

Question

Carlos invested $7,000 in a money market mutual fund that pays interest on a daily basis. The balance in his account at the end of 8 mo (245 days) was $7,432. Find the effective rate at which Carlos's account earned interest over this period (assume a 365-day year). ​

Quizplus · Accepted Answer

We can use the formula:

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

where:
A = ending balance = $7,432
P = principal = $7,000
r = effective interest rate (what we want to find)
n = number of times interest is compounded per year (since it's daily, n = 365)
t = time in years = 8/12 = 2/3

Plug in the values we know and solve for r:

$7,432 = $7,000(1 + r/365)^(365*2/3)
1.062 = (1 + r/365)^(365*2/3)
ln(1.062) = ln(1 + r/365)*(365*2/3)
ln(1.062)/((365*2)/3) = ln(1 + r/365)
0.000561 = ln(1 + r/365)
1.000561 = 1 + r/365
r/365 = 0.000561
r = 0.205% (effective daily rate)
r = 0.205% * 365 = 74.83% (effective annual rate)

Therefore, the answer is B) 9.34%.

Carlos Invested $7,000 in a Money Market Mutual Fund That