Question

Eleven years ago, you deposited $3,200 into an account. Seven years ago, you added an additional $1,000 to this account. You earned 9.2 percent, compounded annually, for the first 4 years and 5.5 percent, compounded annually, for the last 7 years. How much money do you have in your account today?

$8,666.67

$7,717.29

$7,411.90

$8,708.15

$8,073.91

Answer 1

Formula for compound interest:

A = P x (1 + r/m) ^mt

A = Future value of investment

P = Principal

r = Rate of interest

m = No. of compounding in a year

t = No. of years

Value of $ 3,200 after 4 years = $ 3,200 x (1+0.092/1)⁴

                                            = $ 3,200 x (1.092)⁴

                                          = $ 3,200 x 1.4219703913

                                            = $ 4,550.31

$ 4,550.31 is deposited for 7 years at discount rate of 5.5 %

Value of $ 4,550.31 today = $ 4,550.31 x (1+0.055/1)⁷

                                    = $ 4,550.31 x (1.055)⁷

                                      = $ 4,550.31 x 1.4546791611

                                       = $ 6,619.23

Value of $ 1,000 today = $ 1,000 x (1+0.055/1)⁷

                                 = $ 1,000 x (1.055)⁷

                               = $ 1,000 x 1.4546791611

                                 = $ 1,454.68

Total amount in the account today = $ 6,619.23 + $ 1,454.68 = $ 8,073.91

Hence option “$ 8,073.91” is correct answer.