Method I

n = 1 (compounded once every year)

A = P(1 + r)^t

P = $1,200

r = $\frac{5}{100}$ = 0.05

t = 3

A = $1,200(1 + 0.05)³ = $1389.15

Amount earned at the end of the third year = $1389.15

Amount = Principal + Interest

Interest = Amount - Principal

Principal = $1,200

Interest earned at the end of three years = $1389.15 - $1,200

Interest earned at the end of three years = $189.15

Method II

First Year

Principal = $1,200

Time = 1

Rate = 5

Simple Interest = $\frac{\mathrm{\$1200\; x\; 1\; x\; 5}}{100}$ = $60

Amount = Principal + Interest

Amount by the end of the first year = $1200 + $60 = $1260

Second Year

Principal = $1260

Time = 1

Rate = 5

Simple Interest = $\frac{\mathrm{\$1260\; x\; 1\; x\; 5}}{100}$ = $63

Amount by the end of the second year = $1260 + $63 = $1323

Third Year

Principal = $1323

Time = 1

Rate = 5

Simple Interest = $\frac{\mathrm{\$1323\; x\; 1\; x\; 5}}{100}$ = $66.15

Amount by the end of the third year = $1323 + $66.15 = $1389.15

Amount = Principal + Interest

Interest = Amount - Principal

Principal = $1,200

Interest earned at the end of three years = $1389.15 - $1,200

Interest earned at the end of three years = $189.15

Total amount = Principal + Interest

Principal = x

Time = 5

Rate = 2

Simple Interest = $\frac{\mathrm{x\; x\; 5\; x\; 2}}{100}$ = $\frac{\mathrm{10x}}{100}$ = $\frac{\mathrm{x}}{10}$

Total amount = 550,000

Substitute the total amount and the interest into the total amount equation.

550000 = x + $\frac{\mathrm{x}}{10}$

Get rid of the fraction by multiplying both sides by the denominator, 10

550000 x 10 = 10 x x + x

5500000 = 10x + x

5500000 = 11x

Divide both sides by 11

x = $\frac{5500000}{11}$ = ₦ 500,000

Cost of car = ₦5,000,000.00

Deposit = ₦3,000.000.00

Rate = 8% compound intesrest per annum = $\frac{8}{100}$ = 0.08

Balance = ₦5,000,000.00 - ₦3,000,000.00 = ₦2,000,000.00

Hence the interest will only be charged on the ₦2,000,000.00 balance after the first year

Fisrt year

Interest = Principal x Rate x Time

Time = 1 (Compound interest is calculated year by year)

Interest = 0.08 x ₦2,000,000 = ₦160,000

Total amount to be paid by the end of the first year
⇒ ₦2,000,0000 + ₦160,000 = ₦2,160,000

Since he pays ₦1000,000 at each year

Amount left to pay the subsequent year
⇒ ₦2,160,000 - ₦1,000,000 = ₦1,160,000

Second Year

Interest = 0.08 x ₦1,160,000 = ₦92,800

Amount to pay
⇒ ₦92,800 + ₦1,160,000 = ₦1,250,8000

He pays another ₦1,000,000 by the end of the second year.

Hence amount to pay after the second year
⇒ ₦1,252,800 - ₦1,000,000.00 = ₦252,800

NB: For compound interest, the new principal amount is the interest + the previous amount to be paid