Answer: a. To determine the amount in Sydney's account after 10 years, we can use the formula for compound interest:
FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))
where FV is the future value, PMT is the monthly payment, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years.
Plugging in the values for Sydney's account, we get:
FV = 100 × (((1 + 0.05/12)^(12*10) - 1) / (0.05/12))
FV = $16,184.46
Therefore, the amount in Sydney's account after 10 years is $16,184.46.
b. To determine the amount in Benny's account after 10 years, we can use the same formula:
FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))
Plugging in the values for Benny's account, we get:
FV = 80 × (((1 + 0.08/12)^(12*10) - 1) / (0.08/12))
FV = $15,710.21
Therefore, the amount in Benny's account after 10 years is $15,710.21.
c. Sydney had more money in the account after 10 years, since $16,184.46 > $15,710.21.
d. To determine the amount in Sydney's account after 20 years, we can use the same formula:
FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))
Plugging in the values for Sydney's account, we get:
FV = 100 × (((1 + 0.05/12)^(12*20) - 1) / (0.05/12))
FV = $45,074.89
Therefore, the amount in Sydney's account after 20 years is $45,074.89.
e. To determine the amount in Benny's account after 20 years, we can use the same formula:
FV = PMT × (((1 + r/n)^(n*t) - 1) / (r/n))
Plugging in the values for Benny's account, we get:
FV = 80 × (((1 + 0.08/12)^(12*20) - 1) / (0.08/12))
FV = $42,598.05
Therefore, the amount in Benny's account after 20 years is $42,598.05.
f. Sydney had more money in the account after 20 years, since $45,074.89 > $42,598.05.
Explanation: