Question

On May 2, 2019, a $ 25,000 deposit was made into a savings fund that paid 15% interest compounded each month. On October 1, 2019, $ 45,000 was deposited in the account, and that same day the interest rate changed to 16.2% capitalized every two months.

What was the balance on January 1, 2020 if the interest rate changed again on December 1, 2010 to 17% compounded each month?

Answer 1

Formula for compound interest is:

A = P x (1+r/n) nt

A = Final amount

P = Principal amount = $ 25,000

r = Rate of interest = 0.015

n = Number of compounding in a year = 12

t = Number of years amount invested = 5/12 [from 2nd May to 1st Oct]

A = $ 25,000 x (1+0.015/12)5

    = $ 25,000 x (1+0.0125)5

= $ 25,000 x (1.0125)5

= $ 25,000 x 1.06408215362549

= $ 26,602.0538406372 or $ 26,602.05

Fund size on October 1, 2019 = $ 26,602.05 + $ 45,000

                                                  = $ 71,602.05

Interest rate changed to 16.2 % compounded bimonthly.

Accumulated balance on 1st December = $ 71,602.05 x (1+0.162/6)

                                                                  = $ 71,602.05 x (1+0.027)

                                                                   = $ 71,602.05 x (1.027)

                                                                   = $ 73,535.30535

                                                                  

On 1st December interest rate changed to 17 % compounded monthly.

Accumulated balance on 1st January = $ 73,535.30535 x (1+0.17/12)

                                                                  = $ 71,602.05 x (1+0.014166667)

                                                                   = $ 71,602.05 x (1. 014166667)

                                                                   = $ 74,577.05553 or $ 74,577.06

Account balance on 1st January 2020 was $ 74,577.06