At the beginning of year 1, Matilda invests $450 at an annual simple interest rate of 5%. She makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 15? What is the balance?

Question

Miranda Cannon

Mathematics

30 May, 00:45

At the beginning of year 1, Matilda invests $450 at an annual simple interest rate of 5%. She makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 15? What is the balance?

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Answers (1)

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Lilliana Whitney · Answer 1

Given:

Initial investment 450

annual simple interest rate of 5%

Simple interest = Principal * interest rate * term

Simple interest = 450 x 0.05 x 14

Simple Interest = 315

Balance after 14 years: 450 + 315 = $765

We can use compounding interest, compounded once a year.

Total balance = Principal * (1 + interest rate / number of compounding) ^ (# compounding * term)

Total balance = 450 * (1.05) ¹⁴

Total balance = 450 * 1.98

Total balance = 891

Based on these scenarios, the formula that will be used is the second formula, compounding interest formula. The balance at the beginning of year 15 is $891.

I used 14 as the number of years because the problem states at the beginning of year 15. This means 15 has not yet begun and interest is not yet earned.