Question

B2: You deposit $30,000 for 4 years at 7% annual interest. In 4 years, you add $20,000 to your account, but the rate on your account changes to 9% annual interest (for existing balance and new deposit). You leave the account untouched for an additional 15 years. Required: How much money do you accumulate? (SK1: 5 marks

Answer 1

Compound interest will be earned here.

Formula for the final amount (principal + interest) in compounding is given by:

P (1r/n) (nt) A

Where,

A = Final future amount (principal + interest)

P = Initial Principal which we have invested

r = interest rate

n = number of time the interest is compounded [For annual compounding this is equal to 1 ]

t = years

Now for first 4 years

P = $ 30,000

t = 4 years

n = 1

r = 7%

Hence,

A = 30000 ( 1 + 7%) ^ 4

A = 39323.88

Now for next 15 years, we have added additional of $ 20000 and rate is changed

Now,

P = 39323.88 + 20000 = 59323.88

r = 9%

n =1

t = 15 years

Hence, Final amount, A

A = 59323.88 * ( 1 + 9%) ^15

A = 216,086.19