Question

what is the total amount that matthew’s bank will receive after lending him $8,000 for four years at an interest rate of 6 percent, compounded annually?

Answer 1

Answer: Matthew’s bank will receive a total amount of $10,099.82

Explanation:

The total amount the bank will receive can be calculated using the formula: Amount (A) = P(1 + r)^t

Where, P is the principal

r is the rate

and t is time in years

From the question,

Principal (P) = $8000

Rate (r) = 6% = 6/100 = 0.06

Time (t) = 4 years

Hence,

Amount (A) = 8000 × (1 + 0.06)^4

A = 8000 × (1.06)^4

A = 8000 × 1.26247696

A = 10099.81568

Amount (A) = $10,099.82

Hence,

The total amount the bank will receive is $10,099.82

Answer 2

first year the interest will be 6% x 8000= $480
second year the interest will be 6% x 8480= $508.80
third year the interest will be 6% x 8988.80=$539. 33
fourth year the interest will be 6% x 9528.13=$571. 69
the total amount that matthew's bank will receive is 8,000+480+508.80+539.33+571.69=$10,099.82