120k views
4 votes
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.

1 Answer

7 votes

Answer:

(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

User NicoH
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories