You invest $6780 in a floating rate guaranteed investment certificate. For the first 30 months you earn 4.9% compounded semi-annually. For the next 8 months you earn 4.32% compounded monthly. What is the maturity value of the certificate?
A) $7775.44
B) $7785.44
C) $7857.44
D) $7875.44
E) $7888.44

Question

Quizplus · Accepted Answer

To solve the problem, we can use the formula for compound interest:

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

where:
A = maturity value
P = principal (initial investment)
r = interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)

For the first 30 months (2.5 years), we have:
P = $6780
r = 4.9% per year, compounded semi-annually, so we need to divide by 2 to get the rate per compounding period: r = 0.049/2 = 0.0245
n = 2 (semi-annual compounding)
t = 2.5 (30 months divided by 12 months/year)

Plugging in these values, we get:
A = $6780(1 + 0.0245/2)^(2*2.5)
A = $7365.29

For the next 8 months, we have:
P = $7365.29 (this is the new principal, since we're reinvesting the money)
r = 4.32% per year, compounded monthly, so we need to divide by 12 to get the rate per compounding period: r = 0.0432/12 = 0.0036
n = 12 (monthly compounding)
t = 8/12 = 0.6667 (8 months divided by 12 months/year)

Plugging in these values, we get:
A = $7365.29(1 + 0.0036/12)^(12*0.6667)
A = $7875.44

Therefore, the maturity value of the certificate is $7875.44, which is closest to answer D.

You Invest $6780 in a Floating Rate Guaranteed Investment Certificate