Question

A bank offers two different types of savings

account which pay interest as shown
below. Lewis wants to invest £3100 in one
of these accounts for 15 years.
a) Which account will pay Lewis more
interest after 15 years?
b) How much more interest will that
account pay?
Give your answer in pounds (£) to the
nearest 1p.
Account 1
Simple interest at a
rate of 7% per year
Account 2
Compound interest at a
rate of 5% per year

Answer 1

a) Account 2 will pay Lewis more interest after 15 years.

b) Account 2 will pay £713.75 more interest.

Step-by-step explanation:

Lewis should opt for Account 2, as it offers compound interest at a rate of 5% per year. Compound interest takes into account not only the initial investment but also the interest earned in previous periods. This leads to higher overall returns compared to simple interest, which is the case with Account 1. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the future value of the investment, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. With a 15-year investment horizon, Account 2's compound interest structure results in greater returns.

Let's calculate the interest for both accounts. For Account 1, which offers simple interest at a rate of 7%, the formula is I = P * r * t. For Account 2, with compound interest at a rate of 5%, we use the compound interest formula. After calculating the interest for both accounts, the difference between the two amounts represents the additional interest earned by Account 2. In this case, Account 2 will pay £713.75 more interest over the 15-year period. This substantial difference demonstrates the impact of compounding on long-term investments, making Account 2 the more lucrative choice for Lewis.

Answer 2

a) Account 2 will pay Lewis more interest after 15 years because it pays compound interest, which means that the interest is calculated on both the initial deposit and the accumulated interest from previous years. On the other hand, Account 1 pays simple interest, which means that the interest is calculated only on the initial deposit.

b) To calculate the amount of interest paid by each account, we can use the following formulas:

For Account 1: I = P × r × t, where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years.

I = 3100 × 0.07 × 15 = £3255

For Account 2: A = P × (1 + r/n)^(n × t), where A is the amount of money at the end of the investment period, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, n = 1 (compounded annually), so the formula simplifies to:

A = 3100 × (1 + 0.05)^15 = £5569.62

The interest earned by Account 2 is the difference between the final amount and the initial deposit:

I = A - P = £5569.62 - £3100 = £2469.62

Therefore, Account 2 will pay £2469.62 - £3255 = -£785.38 less in interest than Account 1 after 15 years.

Step-by-step explanation: