These are original Marlbridge practice questions, not past exam questions. All questions use Valdoria, a fictional country whose currency is the valda (VD); all people, rates and index numbers are fictional. The rubrics are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. Assumptions: nominal rates are fixed for the length of the loan; real rate = nominal rate − inflation (the course method); a four-function calculator is enough.
Question 1 (multiple choice · foundation)
Which of the following best describes the nominal interest rate on a loan?
- (A) The interest rate paid on the loan, not adjusted for inflation
- (B) The interest rate paid on the loan after subtracting the inflation rate
- (C) The increase in purchasing power the lender receives
- (D) The interest rate set by lenders who expect zero inflation
Answer and explanation
Answer: (A). The nominal rate is the rate written in the loan contract, measured in money and not adjusted for inflation.
- (B) describes the real interest rate.
- (C) is also the real rate: the gain in purchasing power.
- (D) is too narrow. Lenders set a nominal rate whatever inflation they expect; it equals the real rate only when expected inflation is zero.
Question 2 (multiple choice · core)
A Valdorian lender wants an expected real interest rate of 2.5%. Both the lender and the borrower expect inflation of 3.5% over the year. What nominal interest rate will they agree?
- (A) 1.0%
- (B) 2.5%
- (C) 6.0%
- (D) 8.75%
Answer and explanation
Answer: (C). Nominal rate = expected real rate + expected inflation = 2.5% + 3.5% = 6.0%.
- (A) subtracts the two rates (3.5 − 2.5). The lender needs to be compensated for inflation, so it is added.
- (B) is the real rate alone. It ignores the inflation both sides expect.
- (D) multiplies the rates (2.5 × 3.5). The relationship is a sum.
Question 3 (multiple choice · core)
Kofi took out a one-year loan from a Valdorian bank at a nominal interest rate of 5%. Over the year, the actual inflation rate was 7%. What real interest rate did Kofi pay in hindsight?
- (A) −2%
- (B) 2%
- (C) 7%
- (D) 12%
Answer and explanation
Answer: (A). Real rate = nominal rate − actual inflation = 5% − 7% = −2%. The real rate is negative because inflation was higher than the nominal rate.
- (B) subtracts the wrong way round (7 − 5).
- (C) is the inflation rate, not the real rate.
- (D) adds inflation to the nominal rate instead of subtracting it.
Question 4 (multiple choice · core)
In Valdoria, the expected real interest rate stays at 3%, but expected inflation rises from 2% to 6%. What happens to the nominal interest rate on new loans?
- (A) It falls from 1% to −3%.
- (B) It stays at 3%, because the real rate has not changed.
- (C) It rises from 5% to 9%.
- (D) It rises from 3% to 6%.
Answer and explanation
Answer: (C). Before: 3% + 2% = 5%. After: 3% + 6% = 9%. A 4-point rise in expected inflation raises the nominal rate by 4 points when the expected real rate is unchanged.
- (A) subtracts expected inflation from the real rate (3 − 2 and 3 − 6). Lenders add expected inflation to protect their real return.
- (B) confuses the nominal and real rates. Only the real rate stays the same.
- (D) starts from the real rate (3%) and ends at the new expected inflation rate (6%). The nominal rate is the sum of the two, both before and after.
Question 5 (calculation · core)
Valdoria’s CPI and the nominal interest rate on one-year government bonds bought at the start of each year are shown below.
| Year | CPI at end of year | Nominal rate on bonds bought at the start of the year |
|---|---|---|
| 2023 | 240.00 | — |
| 2024 | 252.00 | 6.5% |
| 2025 | 259.56 | 2.5% |
(a) Calculate the inflation rate for 2024 and 2025. (b) Calculate the real interest rate in hindsight for each year. (c) Identify the year in which bondholders lost purchasing power. Explain.
Worked solution
(a) 2024: (252.00 − 240.00) ÷ 240.00 × 100 = 5.00%. 2025: (259.56 − 252.00) ÷ 252.00 × 100 = 3.00%.
(b) 2024: 6.5 − 5.00 = 1.50%. 2025: 2.5 − 3.00 = −0.50%.
(c) 2025. The real rate was negative: the interest (2.5%) did not keep up with the rise in prices (3.00%), so the repaid valdas bought less than the valdas lent.
Common error. Dividing by the new index in 2024 gives 12 ÷ 252 × 100 = 4.76%, which is wrong. Use the earlier index.
Suggested mark points (4): 1 for both inflation rates; 1 each for the two real rates (carried forward from (a) if needed); 1 for (c), which must link the negative real rate to a loss of purchasing power.
Question 6 (constructed response · core)
Tariq borrows VD 18,000 from a Valdorian bank for one year to buy a car. The bank and Tariq both expect inflation of 3% and agree an expected real rate of 4%.
(a) Define the real interest rate. (b) Calculate the nominal interest rate and the interest Tariq pays. (c) Actual inflation over the year is only 1%. Calculate the real interest rate in hindsight. (d) Identify who gains from the lower-than-expected inflation, and explain why. (e) Calculate the nominal rate they would have agreed if they had correctly expected 1% inflation.
Worked solution and suggested Marlbridge rubric
(a) The real interest rate is the interest rate adjusted for inflation. It measures the change in purchasing power for the lender (or the real cost for the borrower).
(b) Nominal rate = 4% + 3% = 7%. Interest = 18,000 × 0.07 = VD 1,260.
(c) Real rate = 7% − 1% = 6%.
(d) The bank (the lender) gains and Tariq loses. The nominal rate included 3 points to cover expected inflation, but prices rose by only 1%. The valdas Tariq repays buy more than both sides planned, so the bank earns a real 6% instead of 4%.
(e) 4% + 1% = 5%.
| Point | What earns it |
|---|---|
| 1 | Definition: interest rate adjusted for inflation (purchasing power) |
| 1 | 7% and VD 1,260 |
| 1 | 6% real rate, using actual inflation |
| 1 | The bank gains, because repayments buy more than expected (lower inflation than built into the rate) |
| 1 | 5% |
“The bank gains” without the reason does not earn the fourth point.
Question 7 (constructed response · stretch)
Amira is comparing two one-year fixed deposits offered by Valdorian banks at different times.
- Deposit A was offered at a time when savers and banks expected inflation of 7%. Its nominal rate was 9%.
- Deposit B was offered at a later time, when expected inflation was 1%. Its nominal rate was 4%.
Compare each deposit using the inflation expected at the time it was offered.
(a) Calculate the expected real interest rate on each deposit. (b) Explain why the deposit with the higher nominal rate is not the better deal. (c) In hindsight, inflation during Deposit A’s year was 8% and during Deposit B’s year was 1.5%. Calculate each real rate in hindsight. (d) For Deposit A, state the nominal rate the bank would have needed to offer for an expected real rate of 3%.
Model answer and suggested Marlbridge rubric
(a) A: 9% − 7% = 2%. B: 4% − 1% = 3%.
(b) A saver cares about purchasing power, not the number of valdas. Most of Deposit A’s 9% only makes up for expected inflation of 7%, leaving 2% of real return. Deposit B leaves 3%. So B is expected to give the larger gain in purchasing power even though its nominal rate is lower.
(c) A: 9% − 8% = 1%. B: 4% − 1.5% = 2.5%. In both cases inflation was higher than expected, so the real rate in hindsight was lower than expected, and the banks (as borrowers of the deposits) gained.
(d) 3% + 7% = 10%.
| Point | What earns it |
|---|---|
| 1 | Both expected real rates (2% and 3%) |
| 1 | Explains that the real rate, not the nominal rate, measures the gain in purchasing power |
| 1 | Both real rates in hindsight (1% and 2.5%), using actual inflation |
| 1 | 10% |
In (c), accept a correct comment on who gained as supporting work, but it is not required for the point.
How did you do?
- Q1 or Q6(a) wrong: re-read “What an interest rate measures” in the study guide.
- Q2, Q4, Q6(b), Q6(e) or Q7(d) wrong: revisit “How lenders and borrowers set a nominal rate” and Worked example 1.
- Q3, Q5 or Q7(c) wrong: revisit “Calculating a real rate in hindsight” and Worked example 2. Check your signs.
- Q6(d) or Q7(b) wrong: look again at who gains when inflation differs from what was expected.
Then tick off the topic checklist.