Answer:
(A) P = 8,500 , r = 0.052 , n = 4
(B) $12203.47
Step-by-step explanation:
* Lets explain how to solve the problem
- The annual percentage rate is R = 5.2%
- The interest is compounded quarterly
- Marcus deposits $8,500
- The account balance can be modeled by the exponential formula
S(t) = P(1 + r/n)^nt, where
# S is the future value
# P is the present value
# r is the annual percentage rate written as a decimal
# n is the number of times each year that the interest is compounded
# t is the time in years
* Lets solve the problem
∵ P is the present value
∵ Marcus deposits $8,500
∴ The present value is 8,500
∵ r is the annual percentage rate written as a decimal
∵ The annual percentage rate is 5.2%
∴ r = 5.2/100 = 0.052
∵ n is the number of times each year that the interest is compounded
∵ The interest is compounded quarterly
∴ n = 4
# (A)
* P = 8,500 , r = 0.052 , n = 4
# (B)
∵ S(t) = P(1 + r/n)^nt
∵ t is the time in years
∵ Marcus invests the money for 7 years
∴ t = 7
∴ S = 8500(1 + 0.052/4)^(4 × 7)
∴ S = 8500(1.013)^28 = 12203.47
* Marcus will have $12203.47 in 7 years
