Question

Interest

1. A savings association pays 1.5% interest quarterly. What is the effective annual interest rate?

2. A sum of money is deposited now in a savings account. The effective annual interest rate is 12% and interest is compounded monthly. How much money must be deposited to yield P500.00 at the end of 11 months?

3. A. 40-year old consulting engineer wants to set up a retirement fund to be used starting at age 65. P20,000.00 is invested now at 6% compounded annually. Approximately how much money will be in the fund at retirement?

4. A bank offers 0.5% effective monthly interest. What is the effective annual rate with monthly compounding?

5. When will an investment of P4,000.00 double if the effective rate is 8% per annum?

Answer 1

Answer:

A savings association pays 1.5% interest quarterly.

hope it helps

Answer 2

1. Annual interest rate = 6.136%

2. invest P 0.4322

3. 85,837.5 will be the retirement fund

Explanation:

1.

We have,

Annual Rate of Return = [(1 + Quarterly Rate of Return)^4] - 1

Here, Quarterly ROR = 1.5% = 0.015

Therefore Annual ROR = $[(1.015)^4] - 1 = 0.06136$

or, Annual interest rate = 6.136%

2.

We have,

Annual Rate of Return = [(1 + Monthly Rate of Return)^12] - 1

Here, Annual ROR = 12%

Therefore $12 = (1+M)^4-1 \implies M = 0.8988\%$

Therefore for A = 500 at 11 months,

$500 = P(1+r)^t \iff 500 = P(1.8988)^1^1 \implies P = 0.4322$

Hence we must invest P 0.4322

3.

We have,

P = 20,000, ROR = 6%, t=25

therefore A = $20000(1.06)^{25} = P\ 85837.4143949$