MATH SOLVE

4 months ago

Q:
# A bank features a savings account that has an annual percentage rate of r=5.2% with interest compounded quarterly. Marcus deposits $8,500 into the account.The account balance can be modeled by the exponential formula S(t)=P(1+rn)^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, and t is the time in years.(A) What values should be used for P, r, and n?P= _____ , r=______ , n=________(B) How much money will Marcus have in the account in 7 years?Answer = $______ .Round answer to the nearest penny.

Accepted Solution

A:

Answer:(A) P = 8,500 , r = 0.052 , n = 4(B) $12203.47Step-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