Question

How long will it take $10,000 to reach $50,000 if it earns 10% annual interest compounded semiannually?

1. 17 years
2. 33 years
3. 16.5 years (correct)
4. 8.5 years

You get a twenty-year amortized loan of $100,000 with a 5% annual interest rate. What are the annual payments?

1. $ 8,718
2. $37,689
3. $ 4,762
4. $ 8,024 (correct)

You get a 25-year loan of $150,000 with an 8% annual interest rate. What are the annual payments?

1. $14,052 (correct)
2. $ 2,052
3. $13,965
4. $13,427

Answer 1

1)

FV = PV * (1+ rate/2) ^number of semi-annual period

50000 = 10000 * (1+0.10/2)^number of semi-annual period

5 = (1+0.10/2)^number of semi-annual period

Taking Log on both side

Log(5) = number of semi-annual period * Log(1+0.05)

Number of semi-annual period = 32.986

Number of years = 16.49 Answer

Option C is correct.

2)

Loan Amount = Present Value of annual payments discounted @5%

Rate =5%

Number of payments = 20

100000 = Annual Payments * (1/(1+0.05)^1 +1/(1+0.05)^2 +1/(1+0.05)^3 +1/(1+0.05)^4 +1/(1+0.05)^5 +1/(1+0.05)^6 +........1/(1+0.05)^20 )

100000 = Annual Payments * 12.46

Annual Payments = 8024.26 Answer

Option D is correct.

3)

Loan Amount = Present Value of annual payments discounted @ 8%

150000 = Annual Payments * (1/(1+0.08)^1 +1/(1+0.08)^2 +1/(1+0.08)^3 +1/(1+0.08)^4 +1/(1+0.08)^5 +1/(1+0.08)^6 +........1/(1+0.08)^25 )

150000 = Annual Payments * 10.67

Annual Payments = 14051.82 Answer

Option A is correct.

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