Question

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.

Answer 1

(A) P = 8,500 , r = 0.052 , n = 4

(B) $12203.47

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